Given the area of 24 square units, the rectangle with dimensions 1 × 24 has the greatest perimeter of 50 units due to its elongated shape. Conversely, the rectangle with dimensions 4 × 6 has the least perimeter of 20 units, as it is closer to a square. Generally, compact shapes like squares minimizeRead more
Given the area of 24 square units, the rectangle with dimensions 1 × 24 has the greatest perimeter of 50 units due to its elongated shape. Conversely, the rectangle with dimensions 4 × 6 has the least perimeter of 20 units, as it is closer to a square. Generally, compact shapes like squares minimize perimeter for a given area, while elongated shapes maximize it.
For an area of 32 square cm, the rectangle with dimensions 1 × 32 has the greatest perimeter of 66 cm, while the one with 4 × 8 has the least perimeter of 24 cm. Compact shapes, such as squares or near-squares, minimize perimeter because the sides are balanced. Elongated shapes, with one very long aRead more
For an area of 32 square cm, the rectangle with dimensions 1 × 32 has the greatest perimeter of 66 cm, while the one with 4 × 8 has the least perimeter of 24 cm. Compact shapes, such as squares or near-squares, minimize perimeter because the sides are balanced. Elongated shapes, with one very long and one short side, maximize perimeter. Thus, the more balanced the dimensions, the smaller the perimeter for a fixed area.
A triangle is a three-sided polygon with three edges and three vertices, forming the simplest closed figure in geometry. Its area represents the space enclosed by its three sides. The formula for the area of a triangle is half the product of its base and height. Mathematically, it is given as (baseRead more
A triangle is a three-sided polygon with three edges and three vertices, forming the simplest closed figure in geometry. Its area represents the space enclosed by its three sides. The formula for the area of a triangle is half the product of its base and height. Mathematically, it is given as (base × height) ÷ 2. This method ensures accurate calculation of the triangular region, irrespective of the triangle’s type or orientation.
When a rectangle is divided by its diagonal, two identical triangles are formed. These triangles can be checked for congruence by overlapping them, and they align perfectly. As the diagonal divides the rectangle into two equal parts, the area of each triangle is exactly half of the rectangle's area.Read more
When a rectangle is divided by its diagonal, two identical triangles are formed. These triangles can be checked for congruence by overlapping them, and they align perfectly. As the diagonal divides the rectangle into two equal parts, the area of each triangle is exactly half of the rectangle’s area. This observation remains true for any rectangle or square, irrespective of its size.
From this exercise, we can infer that the diagonal of a rectangle always divides it into two equal triangles. Both triangles are congruent in shape and size, and their areas are equal to half the area of the rectangle. This principle applies universally to all rectangles and squares, regardless of tRead more
From this exercise, we can infer that the diagonal of a rectangle always divides it into two equal triangles. Both triangles are congruent in shape and size, and their areas are equal to half the area of the rectangle. This principle applies universally to all rectangles and squares, regardless of their dimensions, establishing a consistent relationship between a rectangle and its diagonally divided parts.
Twin primes are pairs of prime numbers that differ by 2. Between 1 and 100, the twin primes are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), and (71, 73). Each pair consists of two primes satisfying the condition of a difference of 2. These pairs highlight the fascinating patterRead more
Twin primes are pairs of prime numbers that differ by 2. Between 1 and 100, the twin primes are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), and (71, 73). Each pair consists of two primes satisfying the condition of a difference of 2. These pairs highlight the fascinating patterns of prime distribution within a specific range.
The statement is true because numbers ending in 4 are even. A prime number has only two divisors: 1 and itself. All even numbers are divisible by 2, making them composite, except for the number 2 itself. Since 2 is the only even prime number, any number with a units digit of 4 cannot be prime. For eRead more
The statement is true because numbers ending in 4 are even. A prime number has only two divisors: 1 and itself. All even numbers are divisible by 2, making them composite, except for the number 2 itself. Since 2 is the only even prime number, any number with a units digit of 4 cannot be prime. For example, numbers like 14, 24, and 34 all have divisors other than 1 and themselves.
The statement is false. A prime number has only two divisors: 1 and itself. The product of two or more primes, such as 2 × 3 = 6, is composite because it has additional divisors beyond 1 and itself (2, 3, and 6). While primes are building blocks for composite numbers, their multiplication always resRead more
The statement is false. A prime number has only two divisors: 1 and itself. The product of two or more primes, such as 2 × 3 = 6, is composite because it has additional divisors beyond 1 and itself (2, 3, and 6). While primes are building blocks for composite numbers, their multiplication always results in numbers with more than two divisors, thereby disqualifying them from being prime.
This statement is false because prime numbers have exactly two factors, which are 1 and the number itself. For example, 13 is a prime number because its only factors are 1 and 13. If a number has no factors other than 1 and itself, it qualifies as prime. The absence of additional factors differentiaRead more
This statement is false because prime numbers have exactly two factors, which are 1 and the number itself. For example, 13 is a prime number because its only factors are 1 and 13. If a number has no factors other than 1 and itself, it qualifies as prime. The absence of additional factors differentiates primes from composite numbers, which have more than two divisors.
The statement is false because not all even numbers are composite. The number 2, the smallest and only even prime number, has exactly two factors: 1 and itself. While other even numbers like 4, 6, and 8 are composite due to having more than two divisors, 2’s unique properties as a prime number makeRead more
The statement is false because not all even numbers are composite. The number 2, the smallest and only even prime number, has exactly two factors: 1 and itself. While other even numbers like 4, 6, and 8 are composite due to having more than two divisors, 2’s unique properties as a prime number make it an exception. Thus, the generalization does not hold for all even numbers.
Which rectangle has the greatest perimeter? b. Which rectangle has the least perimeter?
Given the area of 24 square units, the rectangle with dimensions 1 × 24 has the greatest perimeter of 50 units due to its elongated shape. Conversely, the rectangle with dimensions 4 × 6 has the least perimeter of 20 units, as it is closer to a square. Generally, compact shapes like squares minimizeRead more
Given the area of 24 square units, the rectangle with dimensions 1 × 24 has the greatest perimeter of 50 units due to its elongated shape. Conversely, the rectangle with dimensions 4 × 6 has the least perimeter of 20 units, as it is closer to a square. Generally, compact shapes like squares minimize perimeter for a given area, while elongated shapes maximize it.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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If you take a rectangle of area 32 sq cm, what will your answers be? Given any area, is it possible to predict the shape of the rectangle with the greatest perimeter as well as the least perimeter? Give examples and reasons for your answer.
For an area of 32 square cm, the rectangle with dimensions 1 × 32 has the greatest perimeter of 66 cm, while the one with 4 × 8 has the least perimeter of 24 cm. Compact shapes, such as squares or near-squares, minimize perimeter because the sides are balanced. Elongated shapes, with one very long aRead more
For an area of 32 square cm, the rectangle with dimensions 1 × 32 has the greatest perimeter of 66 cm, while the one with 4 × 8 has the least perimeter of 24 cm. Compact shapes, such as squares or near-squares, minimize perimeter because the sides are balanced. Elongated shapes, with one very long and one short side, maximize perimeter. Thus, the more balanced the dimensions, the smaller the perimeter for a fixed area.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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What do you mean by Triangle? Define Area of a Triangle.
A triangle is a three-sided polygon with three edges and three vertices, forming the simplest closed figure in geometry. Its area represents the space enclosed by its three sides. The formula for the area of a triangle is half the product of its base and height. Mathematically, it is given as (baseRead more
A triangle is a three-sided polygon with three edges and three vertices, forming the simplest closed figure in geometry. Its area represents the space enclosed by its three sides. The formula for the area of a triangle is half the product of its base and height. Mathematically, it is given as (base × height) ÷ 2. This method ensures accurate calculation of the triangular region, irrespective of the triangle’s type or orientation.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
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Check whether the two triangles overlap each other exactly. Do they have the same area?
When a rectangle is divided by its diagonal, two identical triangles are formed. These triangles can be checked for congruence by overlapping them, and they align perfectly. As the diagonal divides the rectangle into two equal parts, the area of each triangle is exactly half of the rectangle's area.Read more
When a rectangle is divided by its diagonal, two identical triangles are formed. These triangles can be checked for congruence by overlapping them, and they align perfectly. As the diagonal divides the rectangle into two equal parts, the area of each triangle is exactly half of the rectangle’s area. This observation remains true for any rectangle or square, irrespective of its size.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-6/
Can you draw any inferences from this exercise?
From this exercise, we can infer that the diagonal of a rectangle always divides it into two equal triangles. Both triangles are congruent in shape and size, and their areas are equal to half the area of the rectangle. This principle applies universally to all rectangles and squares, regardless of tRead more
From this exercise, we can infer that the diagonal of a rectangle always divides it into two equal triangles. Both triangles are congruent in shape and size, and their areas are equal to half the area of the rectangle. This principle applies universally to all rectangles and squares, regardless of their dimensions, establishing a consistent relationship between a rectangle and its diagonally divided parts.
For more NCERT Solutions for Class 6 Math Chapter 6 Perimeter and Area Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-6/
Find twin primes between 1 and 100.
Twin primes are pairs of prime numbers that differ by 2. Between 1 and 100, the twin primes are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), and (71, 73). Each pair consists of two primes satisfying the condition of a difference of 2. These pairs highlight the fascinating patterRead more
Twin primes are pairs of prime numbers that differ by 2. Between 1 and 100, the twin primes are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), and (71, 73). Each pair consists of two primes satisfying the condition of a difference of 2. These pairs highlight the fascinating patterns of prime distribution within a specific range.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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Identify whether each statement is true or false. Explain. a) There is no prime number whose units digit is 4.
The statement is true because numbers ending in 4 are even. A prime number has only two divisors: 1 and itself. All even numbers are divisible by 2, making them composite, except for the number 2 itself. Since 2 is the only even prime number, any number with a units digit of 4 cannot be prime. For eRead more
The statement is true because numbers ending in 4 are even. A prime number has only two divisors: 1 and itself. All even numbers are divisible by 2, making them composite, except for the number 2 itself. Since 2 is the only even prime number, any number with a units digit of 4 cannot be prime. For example, numbers like 14, 24, and 34 all have divisors other than 1 and themselves.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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Identify whether each statement is true or false. Explain. b) A product of primes can also be prime.
The statement is false. A prime number has only two divisors: 1 and itself. The product of two or more primes, such as 2 × 3 = 6, is composite because it has additional divisors beyond 1 and itself (2, 3, and 6). While primes are building blocks for composite numbers, their multiplication always resRead more
The statement is false. A prime number has only two divisors: 1 and itself. The product of two or more primes, such as 2 × 3 = 6, is composite because it has additional divisors beyond 1 and itself (2, 3, and 6). While primes are building blocks for composite numbers, their multiplication always results in numbers with more than two divisors, thereby disqualifying them from being prime.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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Identify whether each statement is true or false. Explain. c) Prime numbers do not have any factors.
This statement is false because prime numbers have exactly two factors, which are 1 and the number itself. For example, 13 is a prime number because its only factors are 1 and 13. If a number has no factors other than 1 and itself, it qualifies as prime. The absence of additional factors differentiaRead more
This statement is false because prime numbers have exactly two factors, which are 1 and the number itself. For example, 13 is a prime number because its only factors are 1 and 13. If a number has no factors other than 1 and itself, it qualifies as prime. The absence of additional factors differentiates primes from composite numbers, which have more than two divisors.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
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Identify whether each statement is true or false. Explain. d) All even numbers are composite numbers.
The statement is false because not all even numbers are composite. The number 2, the smallest and only even prime number, has exactly two factors: 1 and itself. While other even numbers like 4, 6, and 8 are composite due to having more than two divisors, 2’s unique properties as a prime number makeRead more
The statement is false because not all even numbers are composite. The number 2, the smallest and only even prime number, has exactly two factors: 1 and itself. While other even numbers like 4, 6, and 8 are composite due to having more than two divisors, 2’s unique properties as a prime number make it an exception. Thus, the generalization does not hold for all even numbers.
For more NCERT Solutions for Class 6 Math Chapter 5 Prime Time Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-5/