document.write( "Question 655170: find the length of the short leg of a right triangle if the longer leg is 11 feet more than the shorter leg and the hypotenuse is 11 feet less than twice the shorter leg \n" ); document.write( "
Algebra.Com's Answer #408968 by nerdybill(7384)\"\" \"About 
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find the length of the short leg of a right triangle if the longer leg is 11 feet more than the shorter leg and the hypotenuse is 11 feet less than twice the shorter leg
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\n" ); document.write( "Let x = length of shorter leg
\n" ); document.write( "then
\n" ); document.write( "x+11 = longer leg
\n" ); document.write( "2x-11 = hypotenuse
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\n" ); document.write( "Applying Pythagorean's theorem:
\n" ); document.write( "x^2 + (x+11)^2 = (2x-11)^2
\n" ); document.write( "x^2 + (x+11)(x+11) = (2x-11)(2x-11)
\n" ); document.write( "x^2 + (x^2+22x+121) = 4x^2-44x+121
\n" ); document.write( "2x^2+22x+121 = 4x^2-44x+121
\n" ); document.write( "22x+121 = 2x^2-44x+121
\n" ); document.write( "121 = 2x^2-66x+121
\n" ); document.write( "0 = 2x^2-66x
\n" ); document.write( "0 = 2x(x-33)
\n" ); document.write( "x = {0, 33}
\n" ); document.write( "throw out the zero (extraneous) leaving
\n" ); document.write( "x = 33 feet\r
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