document.write( "Question 203547: The side of an equilateral triangle are each s units long. Find the altitude (h) in terms of s. Write the answer in simplest radical form. \n" ); document.write( "

Algebra.Com's Answer #153581 by Earlsdon(6294) $\"\"$ $\"About$

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The altitude bisects the equilateral triangle into two congruent right triangles in which the altitude (of the equilateral triangle) is also the altitude (h) of both right triangles.
\n" ); document.write( "Using the Pythagorean theorem, we can find h in terms of the side (s) of the equilateral triangle.
\n" ); document.write( " $\"h%5E2+=+s%5E2-%28s%2F2%29%5E2\"$ Simplifying.
\n" ); document.write( " $\"h%5E2+=+s%5E2-s%5E2%2F4\"$
\n" ); document.write( " $\"h%5E2+=+%283%2F4%29s%5E2\"$ Taking the square root of both sides, we get:
\n" ); document.write( " $\"highlight%28h+=+%28sqrt%283%29s%29%2F2%29\"$
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