The sides of a triangular plot are in the ratio 3 : 5 : 7 and its perimeter is 300 m. Find its area. Take $\sqrt{3} = 1.732$.

Given,

Sides of a triangle are in the ratio = 3 : 5 : 7

Perimeter = 300 m

Let a = 3x cm, b = 5x cm and c = 7x cm.

Given,

⇒ Perimeter = 300 m

⇒ a + b + c = 300

⇒ 3x + 5x + 7x = 300

⇒ 15x = 300

⇒ x = $\dfrac{300}{15}$ = 20.

Substituting value of x,

a = 3x = 3 × 20 = 60 m,

b = 5x = 5 × 20 = 100 m,

c = 7x = 7 × 20 = 140 m.

We know that,

Semi-perimeter (s) = $\dfrac{\text{Perimeter}}{2} = \dfrac{300}{2}$ = 150 m.

Area of triangle = $\sqrt{s(s - a)(s - b)(s - c)}$

Substituting values we get,

$A = \sqrt{150(150 - 60)(150 - 100)(150 - 140)} \\[1em] = \sqrt{150 \times 90 \times 50 \times 10} \\[1em] = \sqrt{6750000} \\[1em] = 2598.07 ≈ 2598 m^2.$

Hence, area of triangle = 2598 m².