SOLUTION: If you build a deck in the shape of an equilateral triangle with a height of 27ft, how long is one side of the deck?

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Question 1072904: If you build a deck in the shape of an equilateral triangle with a height of 27ft, how long is one side of the deck?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
If by "height" is meant "altitude", then this being in the plane of the deck. cuts this equilateral triangle shape into two congruent special 30-60-90 right triangles.

Do you see? Pythagorean Theorem, and hypotenuse is the length of one side of the deck.


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Half the equilateral triangle, special 30-60-90
leg, 27 feet
leg, x
hypotenuse, 2x
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x%5E2%2B27%5E2=%282x%29%5E2
x%5E2%2B27%5E2=4x%5E2
27%5E2=3x%5E2
3x%5E2=3%2A9%2A27
x%5E2=9%2A27
x%5E2=9%2A9%2A3
x=9sqrt%283%29
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side of the equilateral triangle, 2x=highlight%2818%2Asqrt%283%29%29