document.write( "Question 455467: the hypotenuse of a right triangle is 8feet less then three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. Find the lengths of the three sides of the ttriangle. \n" ); document.write( "
Algebra.Com's Answer #312698 by nerdybill(7384)\"\" \"About 
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the hypotenuse of a right triangle is 8feet less then three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. Find the lengths of the three sides of the ttriangle.
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\n" ); document.write( "Let x = shorter leg
\n" ); document.write( "then
\n" ); document.write( "3x-8 = hypotenuse
\n" ); document.write( "2x+8 = longer leg
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\n" ); document.write( "applying Pythagorean theorem:
\n" ); document.write( "x^2 + (2x+8)^2 = (3x-8)^2
\n" ); document.write( "x^2 + (2x+8)(2x+8) = (3x-8)(3x-8)
\n" ); document.write( "x^2 + (4x^2+16x+16x+64) = (9x^2-24x-24x+64)
\n" ); document.write( "x^2 + 4x^2+32x+64 = 9x^2-48x+64
\n" ); document.write( "5x^2+32x+64 = 9x^2-48x+64
\n" ); document.write( "32x+64 = 4x^2-48x+64
\n" ); document.write( "64 = 4x^2-80x+64
\n" ); document.write( "0 = 4x^2-80x
\n" ); document.write( "0 = x^2-20x
\n" ); document.write( "0 = x(x-20)
\n" ); document.write( "x = {0, 20}
\n" ); document.write( "throw out the zero leaving
\n" ); document.write( "x = 20 feet (shorter leg)
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\n" ); document.write( "hypotenuse:
\n" ); document.write( "3x-8 = 3(20)-8 = 60-8 = 52 feet
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\n" ); document.write( "longer leg:
\n" ); document.write( "2x+8 = 2(20)+8 = 40+8 = 48 feet\r
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