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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.

User Spuder
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1 Answer

6 votes

Answer:

494.34 ft^2

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

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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

The perimeter of a triangle is 170 feet and the sides are in the ratio of 25:14:12. Find-example-1
User Jovita
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