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damaskus [11]
2 years ago
14

A triangular plaque has side lengths of 8 inches, 13 inches, and 15 inches.

Mathematics
1 answer:
lianna [129]2 years ago
6 0
<h3>Answer:  A) 52 square inches</h3>

==========================================================

Explanation:

a = 8, b = 13, and c = 15 are the sides of the triangle

s = (a+b+c)/2 = (8+13+15)/2 = 18 is the semi-perimeter, aka half the perimeter.

Those values are then plugged into Heron's Formula below

A = \sqrt{s*(s-a)*(s-b)*(s-c)}\\\\A = \sqrt{18*(18-8)*(18-13)*(18-15)}\\\\A = \sqrt{18*(10)*(5)*(3)}\\\\A = \sqrt{2700}\\\\A = \sqrt{900*3}\\\\A = \sqrt{900}*\sqrt{3}\\\\A = 30\sqrt{3}\\\\A \approx 51.9615\\\\A \approx 52\\\\

The triangular plaque has an area of approximately 52 square inches.

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