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One leg of a right triangle is 2cm longer than the other leg and 2 cm shorter than the hypotenuse. What is the length of each side?
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\n" ); document.write( "Let x = length of short leg
\n" ); document.write( "then
\n" ); document.write( "x+2 = length of long leg
\n" ); document.write( "x+2+2 = x+4 = length of hypotenuse
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\n" ); document.write( "applying pythagorean:
\n" ); document.write( "x^2 + (x+2)^2 = (x+4)^2
\n" ); document.write( "x^2 + (x+2)(x+2) = (x+4)(x+4)
\n" ); document.write( "x^2 + x^2+4x+4 = x^2+8x+16
\n" ); document.write( "2x^2+4x+4 = x^2+8x+16
\n" ); document.write( "x^2+4x+4 = 8x+16
\n" ); document.write( "x^2-4x+4 = 16
\n" ); document.write( "x^2-4x-12 = 0
\n" ); document.write( "(x-6)(x+2) = 0
\n" ); document.write( "x = {-2,6}
\n" ); document.write( "throw out negative solution (extraneous) leaving
\n" ); document.write( "x = 6 cm (short leg)
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\n" ); document.write( "Long leg:
\n" ); document.write( "x+2 = 6+2 = 8 cm
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\n" ); document.write( "hypotenuse:
\n" ); document.write( "x+4 = 6+4 = 10 cm\r
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