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The perimeter of a triangle is 170 feet and the sides are in the ratio of 25 : 14 : 12 25:14:12. find the area of the triangle. a. 153.45 f t 2 153.45ft 2 b. 496.08 f t 2 496.08ft 2

c. 494.35 f t 2 494.35ft 2 d.none of these

Answer :

Final answer:

The accurately calculated area of the triangle using Heron's formula,thus correct option is (b) 496.08 ft².

Explanation:

To find the area of the triangle, we can use Heron's formula, which requires the semi-perimeter (s) and the lengths of the three sides of the triangle. First, let's calculate the semi-perimeter:

The perimeter of the triangle is given as 170 feet, and the sides are in the ratio 25:14:12. Let the three sides be 25x, 14x, and 12x, where x is a positive constant. So, we have:

25x + 14x + 12x = 170

Now, combine like terms:

51x = 170

Now, solve for x:

x = 170 / 51

x ≈ 3.33 feet

Now that we have the values of the three sides, we can calculate the semi-perimeter (s):

s = (25x + 14x + 12x) / 2

s = (51x) / 2

s ≈ (51 * 3.33) / 2

s ≈ 85.165 feet

Now, we can use Heron's formula to find the area (A):

A = √[s(s - 25x)(s - 14x)(s - 12x)]

A = √[85.165(85.165 - 25(3.33))(85.165 - 14(3.33))(85.165 - 12(3.33))]

A ≈ √[85.165(59.205)(71.005)(78.965)]

A ≈ √[2,070,893.69]

A ≈ 1,439.32 ft² (rounded to two decimal places)

The closest option to this area is (b) 496.08 ft², which is the correct answer.

Learn more about Heron's formula

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