The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Find its area.
Master Class 9th Maths with NCERT solutions and MCQ-based questions from Chapter 10: Heron’s Formula. Solve exercise questions, short-answer problems and detailed explanations to understand how to calculate the area of triangles and quadrilaterals using Heron’s Formula. These resources align with the CBSE syllabus, ensuring complete exam preparation. Regular practice will enhance your problem-solving skills and boost confidence for exams. Access step-by-step solutions and revision notes tailored to simplify learning. Begin practicing today to secure excellent results in exams.
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The sides of the triangular plot are in the ratio 3:5:7, and the perimeter is 300 m. Let the sides be 3x, 5x, and 7x.
From the perimeter:
3x + 5x + 7x = 300 → 15x = 300 → x = 20.
Thus, the sides are:
3x = 60 m, 5x = 100 m, 7x = 140 m.
The semi-perimeter (s) is:
s = Perimeter / 2 = 300 / 2 = 150 m.
Using Heron’s formula for the area of a triangle:
Area = √[s(s-a)(s-b)(s-c)],
where a = 60 m, b = 100 m, c = 140 m.
Substitute the values:
Area = √[150(150-60)(150-100)(150-140)]
= √[150 × 90 × 50 × 10]
= √6750000.
Simplify the square root:
√6750000 = √(2² × 3³ × 5⁶) = 2 × 3¹.⁵ × 5³ = 12√30.
Thus, the area of the triangle is 12√30 m².
This question related to Chapter 10 Mathematics Class 9th NCERT. From the Chapter 10 Heron’s Formula. Probability. Give answer according to your understanding.
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