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

  494.34 ft^2

Step-by-step explanation:

If we assume the given ratio units are actual side lengths, then we can compute the area using Heron's formula:

  A = √(s(s-a)(s-b)(s-c)) . . . . where a, b, c are side lengths, and s=(a+b+c)/2

For this triangle, that area is ...

  s = (25 +14 +12)/2 = 51/2 = 25.5

  A = √(25.5(25.5 -25)(25.5 -14)(25.5 -12)) = √(25.5·0.5·11.5·13.5) = √1979.4375

  A ≈ 44.4909 . . . . square ratio units

__

The perimeter in ratio units is 2s = 51. The actual perimeter is 170 feet, so the scale factor between ratio units and feet is ...

  (170 ft)/(51 ratio units) = (10/3) ft/ratio unit

The area scale factor is the square of this, so the area in square feet is ...

  (44.4909 units^2)(10/3 ft/unit)^2 = 494.34 ft^2

step-by-step explanation: