document.write( "Question 56484: Hello! I need help solving the following please...In a right triangle one side is 1 unit longer than the other side and the perimeter is 12 feet. Find the length of the hypotenuse. Thanks! \n" ); document.write( "
Algebra.Com's Answer #38316 by stanbon(75887)\"\" \"About 
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In a right triangle one side is 1 unit longer than the other side and the perimeter is 12 feet. Find the length of the hypotenuse.
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\n" ); document.write( "Let one leg be \"x\".
\n" ); document.write( "The other leg is \"x+1\"
\n" ); document.write( "Let the hypotenuse be \"h\"
\n" ); document.write( "EQUATION:
\n" ); document.write( "Perimeter: x+x+1+h=12 ft.
\n" ); document.write( "1st: 2x+h=11
\n" ); document.write( "Pythagoras: x^2+(x+1)^2=h^2
\n" ); document.write( "x^2+x^2+2x+1=h^2
\n" ); document.write( "2x^2+2x+1 = h^2
\n" ); document.write( "2nd: h=sqrt(2x^2+2x+1)
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\n" ); document.write( "Solve 1st for h:
\n" ); document.write( "3rd: h=-2x+11
\n" ); document.write( "Substitute for \"h\" in 2nd:
\n" ); document.write( "-2x+11=sqrt(2x^2+2x+1)
\n" ); document.write( "Square both sides to get:
\n" ); document.write( "4x^2-44x+121 = 2x^2+2x+1
\n" ); document.write( "2x^2-46x+120=0
\n" ); document.write( "x^2-23x+60=0
\n" ); document.write( "(x-20)(x-3)=0
\n" ); document.write( "x-20 or x=3
\n" ); document.write( "If x=20 cannot be an answer because the perimeter is 12.
\n" ); document.write( "If x=3, h=-2(3)+11 = 5 ft
\n" ); document.write( "Hypotenuse is 5 ft.
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "
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