Question 562536
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The altitude of an equilateral triangle forms a 30-60-90 right triangle where the side of the equilateral triangle is the hypotenuse and the altitude is the long leg.  The sides of a 30-60-90 right triangle are in proportion *[tex \Large 1\,:\,\frac{\sqrt{3}}{2}\,:\,\frac{1}{2}].  Hence, if the side of the equilateral triangle measures *[tex \Large x], then the altitude must measure *[tex \Large \frac{x\sqrt{3}}{2}].


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sqrt{3}}{2}x\ =\ 12]


A little algebra music, Sammy:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 8\sqrt{3}]


Now that you have one side of your equilateral triangle, you should be able to compute the perimeter yourself.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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