SOLUTION: The problem I need help solving reads " Find the side of an equilateral triangle whose altitude is 8 sqrt of 3"

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Question 202551: The problem I need help solving reads " Find the side of an equilateral triangle whose altitude is 8 sqrt of 3"
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
If you draw a diagram of this problem, you will see the the altitude of the equilateral triangle bisects the base of the triangle thus dividing the equilateral triangle into two congruent right triangles.
Let the side of the equilateral triangle be x.
Then half the base will be x%2F2 and the height is given as h+=+8sqrt%283%29.
So we now have the three sides of one of the right triangles (x (the hypotenuse)), (x/2 (the base)), and (8sqrt%283%29 (the height)), two of them in terms of x, so we can use the Pythagorean theorem c%5E2+=+a%5E2%2Bb%5E2 to find the value of x.
x%5E2+=+%28x%2F2%29%5E2%2B%288%2Asqrt%283%29%29%5E2
x%5E2+=+x%5E2%2F4+%2B+64%2A3
x%5E2+=+x%5E2%2F4+%2B+192 Multiply through by 4 to clear the fraction.
4x%5E2+=+x%5E2%2B768 Subtract x%5E2 from both sides.
3x%5E2+=+768 Divide both sides by 3.
x%5E2+=+256 Take the square root of both sides.
highlight%28x+=+16%29
The side of the equilateral triangle is 16.