document.write( "Question 888505: The hypotenuse of the right triangle is 26. One leg is 4 more than twice the other leg. Determine the length of the longer leg. \n" ); document.write( "
Algebra.Com's Answer #537487 by Theo(13342)\"\" \"About 
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let x = one of the legs.
\n" ); document.write( "let y = the other leg.
\n" ); document.write( "pythagorus says:
\n" ); document.write( "x^2 + y^2 = 26^2
\n" ); document.write( "y = 2x + 4
\n" ); document.write( "x^2 + y^2 = 26^2 becomes:
\n" ); document.write( "x^2 + (2x+4)^2 = 26^2
\n" ); document.write( "simplify to get:
\n" ); document.write( "x^2 + 4x^2 + 16x + 16 = 676
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "5x^2 + 16x + 16 = 676
\n" ); document.write( "subtract 676 from both sides to get:
\n" ); document.write( "5x^2 + 16x - 660 = 0
\n" ); document.write( "factor to get:
\n" ); document.write( "(x-10)(5x+66) = 0
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = 10 or x = -66/5
\n" ); document.write( "x can't be negative, so x = 10
\n" ); document.write( "if x = 10, then 2x+4 = 24
\n" ); document.write( "x = 10
\n" ); document.write( "y = 24
\n" ); document.write( "10^2 + 24^2 = 100 + 576 = 676 = 26^2
\n" ); document.write( "all is good.
\n" ); document.write( "one leg is 10.
\n" ); document.write( "the other leg is 24.
\n" ); document.write( "the leg of 24 is 4 more than twice the leg of 10.\r
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