document.write( "Question 821288: What is the perimeter of a 45°-45°-90° triangle if the hypotenuse is equal to 16 feet? \n" ); document.write( "

Algebra.Com's Answer #494067 by KMST(5328) $\"\"$ $\"About$

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That is an isosceles right triangle.
\n" ); document.write( "The sides opposite the congruent $\"45%5Eo\"$ angles are congruent.
\n" ); document.write( "Those are the legs of the right triangle.
\n" ); document.write( "If the length of each of those legs is $\"x\"$ $\"feet\"$ ,
\n" ); document.write( "and the hypotenuse measures $\"16feet\"$ ,
\n" ); document.write( "then according to the Pythagorean theorem
\n" ); document.write( " $\"x%5E2%2Bx%5E2=16%5E2\"$
\n" ); document.write( " $\"2x%5E2=16%5E2\"$
\n" ); document.write( " $\"x%5E2=16%5E2%2F2\"$
\n" ); document.write( " $\"x%5E2=%288%2A2%29%5E2%2F2\"$
\n" ); document.write( " $\"x%5E2=8%5E2%2A2%5E2%2F2\"$
\n" ); document.write( " $\"x%5E2=8%5E2%2A2\"$
\n" ); document.write( " $\"x=sqrt%288%5E2%2A2%29\"$
\n" ); document.write( " $\"x=8sqrt%282%29\"$
\n" ); document.write( "The, the perimeter is
\n" ); document.write( " $\"8sqrt%282%29%2B8sqrt%282%29%2B16=16sqrt%282%29%2B16\"$ = $\"highlight%2816%281%2Bsqrt%282%29%29%29\"$ = $\"highlight%28about38.6%29\"$ (rounded)
\n" ); document.write( "So the perimeter is about $\"highlight%2838.6feet%29\"$ . \n" ); document.write( "

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