document.write( "Question 801311: if the length of the hypotenuse of a 30-60-90 triangle is 7 square root of 2 what's the area and perimeter. I have to find proofs for the problem for modern geometry class. \n" ); document.write( "

Algebra.Com's Answer #483518 by josgarithmetic(39620) $\"\"$ $\"About$

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Draw the triangle. This is half of an equilateral triangle. The hypotenuse of the 30-60-90 triangle is two times the short leg. \r
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\n" ); document.write( "\n" ); document.write( "Let y=height
\n" ); document.write( "Let x=short leg
\n" ); document.write( "Already known, $\"7sqrt%282%29+=+h\"$ , hypotenuse, same as side of equilateral triangle.\r
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\n" ); document.write( "\n" ); document.write( "As property of 30-60-90 triangle, $\"h=2x\"$ .
\n" ); document.write( "According to pythagorean theorem, $\"x%5E2%2By%5E2=h%5E2\"$
\n" ); document.write( "We already know h, so we want to use the h relationship formula to make equation with only one unknown variable in the pythagorean theorem relationship.
\n" ); document.write( " $\"x=h%2F2\"$ , so substitute:
\n" ); document.write( " $\"%28h%2F2%29%5E2%2By%5E2=h%5E2\"$
\n" ); document.write( " $\"y%5E2=h%5E2-%28h%2F2%29%5E2\"$
\n" ); document.write( " $\"y%5E2=4h%5E2%2F4-h%5E2%2F4=%281%2F4%29%284h%5E2-h%5E2%29\"$
\n" ); document.write( " $\"y%5E2=%28h%5E2%2F4%29%283%29\"$
\n" ); document.write( " $\"y=%28h%2F2%29sqrt%283%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now go back and find $\"x=h%2F2\"$ . You will find area as $\"%281%2F2%29%28h%2F2%29%28%28h%2F2%29sqrt%283%29%29\"$ which is simply $\"%281%2F2%29%2Abase%2Aheight\"$ . \n" ); document.write( "

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