Question

The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle.

Answer 1

The sides of a triangle are in the ratio 25 : 17 : 12

Let the sides of a triangle area a = 25x, b = 17x and c = 12x say.

Perimeter = 25 = a + b + c = 540 cm

⇒ 25x + 17x + 12x = 540 cm

⇒ 54x = 540 cm

⇒ x = `540/54`

⇒ x = 10 cm

∴ The sides of a triangle are a = 250 cm, b = 170 cm and c = 120 cm

Now, Semi perimeter `s =(a + b + c)/2`

= `540/2`

= 270 cm

∴ The area of the triangle = `sqrt(s(s - a)(s - b)(s - c))`

= `sqrt(270(270-250)(270-170)(270-120))`

= `sqrt(27(20)(100)(150))`

= `sqrt((9000)(9000))`

= 9000 cm²

The area of triangle = 9000 cm².