SOLUTION: If an equilateral triangle has a height of 8.5 inches, how long is each side? Plus formula please

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Question 959628: If an equilateral triangle has a height of 8.5 inches, how long is each side? Plus formula please
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The height cuts the equilateral triangle into two 30-60-90 special triangles.

x, the side of the equilateral triangle.
x%5E2=%288.5%29%5E2%2B%28x%2F2%29%5E2----Pythagorean Theorem Relationship
x%5E2=%281%2F4%29x%5E2%2B8.5%5E2
%283%2F4%29x%5E2=8.5%5E2
x%5E2=%288.5%5E2%29%2F%283%2F4%29
x%5E2=%284%2F3%29%2817%2F2%29%5E2
x=%282%2A17%29%2F%282%2Asqrt%283%29%29
highlight%28x=17%2Fsqrt%283%29%29------rationalize if you want.