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Geometry

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A 30-60-90 triangle is drawn on the exterior of an equilateral triangle so the hypotenuse of the right triangle is one side of the equilateral triangle. If the shorter leg of the right triangle is 6 units, what is the perimeter of the equilateral triangle?

Jun 19, 2022

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Recall that in a 30-60-90 triangle, the hypotenuse is double the length of the shortest side.

This means that one side of the triangle is 12 units, meaning the total perimeter is $$12 \times 3 = \color{brown}\boxed{36}$$

Jun 19, 2022