Question

sides of a triangle are in ratio12:17:25 and it's perimeter is 540 cm.find area by heron's formula​

Answer 1

Ratio of the sides of the triangle = 12 : 17 : 25Let the common ratio be x then sides are 12x, 17x and 25xPerimeter of the triangle = 540cm12x + 17x + 25x = 540 cm⇒ 54x = 540cm⇒ x = 10Sides of triangle are,12x = 12 × 10 = 120cm17x = 17 × 10 = 170cm25x = 25 × 10 = 250cmSemi perimeter of triangle(s) = 540/2 = 270cmUsing heron's formula,Area of the triangle = √s (s-a) (s-b) (s-c) = √270(270 - 120) (270 - 170) (270 - 250)cm2 = √270 × 150 × 100 × 20 cm2 = 9000 cm2