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

⇒Let x be common ratio
∴Sides of triangle will be: 12x, 17x and 25x
⇒Perimeter = 540 cm (given)
⇒12x + 17x + 25x = 540 cm,
⇒54x = 540 cm
⇒x = 10 cm
∴Sides of triangle: a = 120, b = 170, c = 250 cms
⇒2S = 540
⇒S = 270 cm
A = √s(s-a)(s-b)(s-c) = √270(270-120)(270-170)(270-250) cm² = √270 × 150 × 100 × 20 cm² = √3 × 3 × 3 × 10 × 5 × 3 × 10 × 100 × 5 × 4 cm² = 3 × 3 × 10 × 10 × 5 × 2
A = 9000 cm²