The sides of a triangular plot are in the ratio 3 : 5 : 7; its perimeter is 300 m. Find its area.                 [Page No. 142]

Let sides be $3k, 5k, 7k$.

Perimeter = $3k + 5k + 7k = 15k = 300$

$$\therefore k = 20$$

Sides: $a = 60 \text{ m}$, $b = 100 \text{ m}$, $c = 140 \text{ m}$

Using Heron's formula:

$$\begin{aligned} A &= \sqrt{150(150-60)(150-100)(150-140)} \\ &= \sqrt{150 \times 90 \times 50 \times 10} \\ &= \sqrt{6750000} = 1500\sqrt{3} \text{ m}^2 \end{aligned}$$

Concept Applied
Heron’s formula gives the area of any triangle from its three sides $\sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semi-perimeter.