The sides of a triangular plot are in the ratio 3 : 5 : 7; its perimeter is 300 m. Find its area. Class 9

The sides of a triangular plot are in the ratio 3 : 5 : 7; its perimeter is 300 m. Find its area. Class 9

Question 1.

The sides of a triangular plot are in the ratio 3 : 5 : 7; its perimeter is 300 m. Find its area. Class 9

Solution:

Ratio of sides of triangular plot is = 3 : 5 : 7,

Let sides of triangular plot be,

3x, 5x, 7x m

∵ Perimeter = 300 m ... [Given]

∴ 3x + 5x + 7x = 300

∴ 15x = 300

∴ x = 20

∴ Sides of triangular plot are 60 m, 100 m and 140 m.

∴ Semi-perimeter (s) = $\frac{300}{2}$ = 150 m

Area of triangle by Heron's formula

$\begin{aligned} & =\sqrt{s(s-a)(s-b)(s-c)} \\ & =\sqrt{150(150-60)(150-100)(150-140)} \\ & =\sqrt{150 \times 90 \times 50 \times 10} \\ & =100 \sqrt{675} \\ & =100 \sqrt{225 \times 3} \\ & =100 \times 15 \sqrt{3} \\ & =1500 \sqrt{3}\end{aligned}$

∴ Area of the triangular plot = $1500 \sqrt{3}$ cm²