document.write( "Question 1055409: Find the length of the shorter leg of a right triangle if the longer leg is 8 feet more than the shorter leg and the hypotenuse is 8feet less than twice the shorter leg \n" ); document.write( "

Algebra.Com's Answer #670621 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "Find the length of the shorter leg of a right triangle if the longer leg is 8 feet more than the shorter leg
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document.write( "Let x = the length (in ft) of the shorter leg of a right triangle.\r\n" );
document.write( "Then the longer leg is (x+8) feet.\r\n" );
document.write( "The hypotenuse is 2x-8.\r\n" );
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document.write( "The Pythagorean theorem says\r\n" );
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document.write( "x^2 + (x+8)^2 = (2x-8)^2.\r\n" );
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document.write( "Simplify and solve for x:\r\n" );
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document.write( " = ,\r\n" );
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document.write( "2x^2 - 48x = 0,\r\n" );
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document.write( "x^2 - 24x = 0,\r\n" );
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document.write( "x(x-24) = 0.\r\n" );
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document.write( "The shorter leg is 24 ft. The longer leg is 32 ft. The hypotenuse is 2*24-8 = 40 ft.\r\n" );
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document.write( "And the check is 24^2 + 32^2 = 40^2.\r\n" );
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document.write( "It is (3,4,5)-right-angled triangle.\r\n" );
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