document.write( "Question 202551: 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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Algebra.Com's Answer #152753 by Earlsdon(6294) $\"\"$ $\"About$

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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.
\n" ); document.write( "Let the side of the equilateral triangle be x.
\n" ); document.write( "Then half the base will be $\"x%2F2\"$ and the height is given as $\"h+=+8sqrt%283%29\"$ .
\n" ); document.write( "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.
\n" ); document.write( " $\"x%5E2+=+%28x%2F2%29%5E2%2B%288%2Asqrt%283%29%29%5E2\"$
\n" ); document.write( " $\"x%5E2+=+x%5E2%2F4+%2B+64%2A3\"$
\n" ); document.write( " $\"x%5E2+=+x%5E2%2F4+%2B+192\"$ Multiply through by 4 to clear the fraction.
\n" ); document.write( " $\"4x%5E2+=+x%5E2%2B768\"$ Subtract $\"x%5E2\"$ from both sides.
\n" ); document.write( " $\"3x%5E2+=+768\"$ Divide both sides by 3.
\n" ); document.write( " $\"x%5E2+=+256\"$ Take the square root of both sides.
\n" ); document.write( " $\"highlight%28x+=+16%29\"$
\n" ); document.write( "The side of the equilateral triangle is 16. \n" ); document.write( "

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