In ΔABC, points D and E are on sides AB and AC respectively, with DE parallel to BC. Given that: - AD = 3 cm - DB = 2 cm - DE || BC According to the Basic Proportionality Theorem (BPT): - When a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides those sidesRead more
In ΔABC, points D and E are on sides AB and AC respectively, with DE parallel to BC.
Given that:
– AD = 3 cm
– DB = 2 cm
– DE || BC
According to the Basic Proportionality Theorem (BPT):
– When a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides those sides in the same ratio
– Therefore, AD:DB = AE:EC = 3:2
While we know the ratio AE:EC = 3:2, we cannot determine the actual length of AE because:
1. The total length of AC is unknown
2. Without knowing AC, we cannot split it in the ratio 3:2 to find AE
3. Having just the ratio 3:2 and no information about the total length AC means there could be infinitely many possible values for AE
For example:
– If AC = 10 cm, then AE would be 6 cm
– If AC = 15 cm, then AE would be 9 cm
– If AC = 5 cm, then AE would be 3 cm
Therefore, the length of AE cannot be determined with the given information.
When two triangles are similar (ΔABC ~ ΔDEF), their areas and sides follow a particular mathematical relationship: If area ratio = m:n, then side ratio = √m:√n Given: - ΔABC ~ ΔDEF - ar(ABC):ar(DEF) = 16:25 Therefore: 1. The side ratio is obtained by square root of the area ratio 2. Side ratio = √16Read more
When two triangles are similar (ΔABC ~ ΔDEF), their areas and sides follow a particular mathematical relationship:
If area ratio = m:n, then side ratio = √m:√n
Given:
– ΔABC ~ ΔDEF
– ar(ABC):ar(DEF) = 16:25
Therefore:
1. The side ratio is obtained by square root of the area ratio
2. Side ratio = √16:√25
3. Simplifying: 4:5
AB:DE = 4:5
This relationship holds because:
– Area ratio = (Side ratio)²
– Suppose side ratio = x:y, then area ratio = x²:y²
– In a similar vein, if area ratio = m:n, then side ratio = √m:√n
– Now, in this example, √16:√25 = 4:5
The above mathematical equivalence applies to every pair of similar triangles because area ratio is always equal to the square of ratio of the respective sides.
In two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. Given that the ratio of the corresponding sides is 4:9, the ratio of their areas can be calculated as: (Ratio of areas ) = ( Ratio of sides )² = ( 4:9 )² = 4² : 9² = 16:81 Thus, the cRead more
In two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Given that the ratio of the corresponding sides is 4:9, the ratio of their areas can be calculated as:
(Ratio of areas ) = ( Ratio of sides )²
= ( 4:9 )²
= 4² : 9²
= 16:81
Since ΔABC and ΔDEF are similar, the corresponding sides of the triangles are in proportion. That is: AB / DE = BC / EF It is provided that 2 AB = DE, i.e., DE / AB = 2 Therefore, the ratio of the corresponding sides of the triangles is 1:2 (AB:DE). Based on this ratio, we can express: BC / EF = 1 /Read more
Since ΔABC and ΔDEF are similar, the corresponding sides of the triangles are in proportion. That is:
AB / DE = BC / EF
It is provided that 2 AB = DE, i.e.,
DE / AB = 2
Therefore, the ratio of the corresponding sides of the triangles is 1:2 (AB:DE). Based on this ratio, we can express:
BC / EF = 1 / 2
Substituting BC = 8 cm:
8 / EF = 1 / 2
Divide both sides by 8:
EF = 2
EF = 8 × 2
EF = 16 cm
So, the answer is 16 cm.
To calculate the power of the engine, we can use the formula for power related to the flow of water through the hose: Power (P) = (mass flow rate) × (velocity)² / 2 Step 1: Calculate the mass flow rate Mass per unit length of water = 100 kg/m Velocity of water = 2 m/s The mass flow rate (ṁ) can be cRead more
To calculate the power of the engine, we can use the formula for power related to the flow of water through the hose:
Power (P) = (mass flow rate) × (velocity)² / 2
Step 1: Calculate the mass flow rate
Mass per unit length of water = 100 kg/m
Velocity of water = 2 m/s
The mass flow rate (ṁ) can be calculated as:
ṁ = (mass per unit length) × (velocity)
ṁ = 100 kg/m × 2 m/s
ṁ = 200 kg/s
Step 2: Calculate the power
Now using the power formula:
P = (ṁ × v²) / 2
P = (200 kg/s × (2 m/s)²) / 2
P = (200 kg/s × 4 m²/s²) / 2
P = (800 kg·m²/s³) / 2
P = 400 W
If in ΔABC, D and E are points on sides AB and AC respectively such that DE || BC and AD = 3 cm, DB = 2 cm, then AE equals:
In ΔABC, points D and E are on sides AB and AC respectively, with DE parallel to BC. Given that: - AD = 3 cm - DB = 2 cm - DE || BC According to the Basic Proportionality Theorem (BPT): - When a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides those sidesRead more
In ΔABC, points D and E are on sides AB and AC respectively, with DE parallel to BC.
Given that:
– AD = 3 cm
– DB = 2 cm
– DE || BC
According to the Basic Proportionality Theorem (BPT):
– When a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides those sides in the same ratio
– Therefore, AD:DB = AE:EC = 3:2
While we know the ratio AE:EC = 3:2, we cannot determine the actual length of AE because:
1. The total length of AC is unknown
2. Without knowing AC, we cannot split it in the ratio 3:2 to find AE
3. Having just the ratio 3:2 and no information about the total length AC means there could be infinitely many possible values for AE
For example:
– If AC = 10 cm, then AE would be 6 cm
– If AC = 15 cm, then AE would be 9 cm
– If AC = 5 cm, then AE would be 3 cm
Therefore, the length of AE cannot be determined with the given information.
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If ΔABC ~ ΔDEF, and ar(ABC):ar(DEF) = 16:25, then AB:DE equals:
When two triangles are similar (ΔABC ~ ΔDEF), their areas and sides follow a particular mathematical relationship: If area ratio = m:n, then side ratio = √m:√n Given: - ΔABC ~ ΔDEF - ar(ABC):ar(DEF) = 16:25 Therefore: 1. The side ratio is obtained by square root of the area ratio 2. Side ratio = √16Read more
When two triangles are similar (ΔABC ~ ΔDEF), their areas and sides follow a particular mathematical relationship:
If area ratio = m:n, then side ratio = √m:√n
Given:
– ΔABC ~ ΔDEF
– ar(ABC):ar(DEF) = 16:25
Therefore:
1. The side ratio is obtained by square root of the area ratio
2. Side ratio = √16:√25
3. Simplifying: 4:5
AB:DE = 4:5
This relationship holds because:
– Area ratio = (Side ratio)²
– Suppose side ratio = x:y, then area ratio = x²:y²
– In a similar vein, if area ratio = m:n, then side ratio = √m:√n
– Now, in this example, √16:√25 = 4:5
The above mathematical equivalence applies to every pair of similar triangles because area ratio is always equal to the square of ratio of the respective sides.
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See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-6/
If in two similar triangles, the ratio of their corresponding sides is 4:9, then the ratio of their areas is:
In two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. Given that the ratio of the corresponding sides is 4:9, the ratio of their areas can be calculated as: (Ratio of areas ) = ( Ratio of sides )² = ( 4:9 )² = 4² : 9² = 16:81 Thus, the cRead more
In two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Given that the ratio of the corresponding sides is 4:9, the ratio of their areas can be calculated as:
(Ratio of areas ) = ( Ratio of sides )²
= ( 4:9 )²
= 4² : 9²
= 16:81
Thus, the correct answer is 16:81.
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If ΔABC and ΔDEF are similar such that 2 AB = DE and BC = 8 cm, then EF =
Since ΔABC and ΔDEF are similar, the corresponding sides of the triangles are in proportion. That is: AB / DE = BC / EF It is provided that 2 AB = DE, i.e., DE / AB = 2 Therefore, the ratio of the corresponding sides of the triangles is 1:2 (AB:DE). Based on this ratio, we can express: BC / EF = 1 /Read more
Since ΔABC and ΔDEF are similar, the corresponding sides of the triangles are in proportion. That is:
AB / DE = BC / EF
It is provided that 2 AB = DE, i.e.,
DE / AB = 2
Therefore, the ratio of the corresponding sides of the triangles is 1:2 (AB:DE). Based on this ratio, we can express:
BC / EF = 1 / 2
Substituting BC = 8 cm:
8 / EF = 1 / 2
Divide both sides by 8:
EF = 2
EF = 8 × 2
EF = 16 cm
So, the answer is 16 cm.
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An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine?
To calculate the power of the engine, we can use the formula for power related to the flow of water through the hose: Power (P) = (mass flow rate) × (velocity)² / 2 Step 1: Calculate the mass flow rate Mass per unit length of water = 100 kg/m Velocity of water = 2 m/s The mass flow rate (ṁ) can be cRead more
To calculate the power of the engine, we can use the formula for power related to the flow of water through the hose:
Power (P) = (mass flow rate) × (velocity)² / 2
Step 1: Calculate the mass flow rate
Mass per unit length of water = 100 kg/m
Velocity of water = 2 m/s
The mass flow rate (ṁ) can be calculated as:
ṁ = (mass per unit length) × (velocity)
ṁ = 100 kg/m × 2 m/s
ṁ = 200 kg/s
Step 2: Calculate the power
Now using the power formula:
P = (ṁ × v²) / 2
P = (200 kg/s × (2 m/s)²) / 2
P = (200 kg/s × 4 m²/s²) / 2
P = (800 kg·m²/s³) / 2
P = 400 W
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