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).
