Question

Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.

Answer 1

Let the common ratio between the sides of the given triangle be x.

Therefore, the side of the triangle will be 12x, 17x, and 25x.

Perimeter of this triangle = 540 cm

12x + 17x + 25x = 540 cm

54x = 540 cm

x = 10 cm

Sides of the triangle will be 120 cm, 170 cm, and 250 cm.

s = `"perimeter of triangle"/2`

= `540/2`

= 270 cm

By Heron's formula,

Area of triangle = `sqrt(s(s-a)(s-b)(s-c))`

= `[sqrt(270(270-120)(270-170)(270-250))]cm^2`

= `[sqrt(270xx150xx100xx20)]cm^2`

= `sqrt(10^2 xx 10^2 xx 3^2 xx 3^2 xx 5^2 xx 2^2)  cm^2`

= (10 × 10 × 3 × 3 × 5 × 2) cm²

= 9,000 cm²

Therefore, the area of this triangle is 9,000 cm².