According to the given ratio, the lengths of the sides are:
25x + 14x + 12x equals 170
51x equals 170
x equals 170 divided by 51
x equals 3 1/3
Thus, the lengths of the sides are: 25 times 3 1/3 equals 83 1/3 feet.
14 times 3 1/3 equals 46 2/3 feet.
12 times 3 1/3 equals 40 feet.
By employing Heron’s formula,
the semi-perimeter (S) is calculated as 170 divided by 2, yielding 85 ft.
Thus, the area of the triangle is given by SQRT(S*(S-83 1/3)*(S-46 2/3)*(S-40)).
This results in SQRT(85*(85-83 1/3)*(85-46 2/3)*(85-40)).
This simplifies to SQRT(85*1 2/3*38 1/3*45).
= SQRT(244374).
= 494.34 square feet (round as necessary).