Question

The perimeter of a triangle is 170 ft and the sides are in the ratio of 25:14:12. Find the area of the triangle

Answer 1

using the ratio, the length of the sides are:

25x + 14x + 12x = 170

51x = 170

x = 170 / 51

x = 3 1/3

The lengths of the sides are: 25 * 3 1/3 = 83 1/3 feet

14 x 3 1/3 = 46 2/3 feet

12 x 3 1/3 = 40 feet

Using Heron's formula

the semi perimeter (S) = 170/2 = 85 ft.

The area of the triangle = SQRT(S*(S-83 1/3) * (S - 46 2/3) * (S-40))

= SQRT (85 * (85-83 1/3) * (85 - 46 2/3) * (85-40)

= SQRT (85 * 1 2/3 * 38 1/3 * 45)

= SQRT(244374)

= 494.34 square feet ( round answer as needed).