document.write( "Question 1138312: The longer leg of a right triangle is
\n" ); document.write( "1 ft longer than the shorter leg. The hypotenuse is 9ft
\n" ); document.write( "longer than the shorter leg. Find the side lengths of the triangle. \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #756141 by ikleyn(52806) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "Let x be the longer leg length (in feet).\r\n" );
document.write( "\r\n" );
document.write( "Then the shorter leg is (x-1) feet long; the hypotenuse is (x+8) feet long.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "According to the Pythagorean theorem,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     +  = ,   or\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     = \r\n" );
document.write( "\r\n" );
document.write( "     = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor the quadratic polynomial on the left side\r\n" );
document.write( "\r\n" );
document.write( "    (x-21)*(x+3) = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Its roots are x= 21 and  x= -3,  but only positive solution is meaningful.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The longer leg is 21 ft;  the shorter leg is  21-1 = 20 ft.\r\n" );
document.write( "\r\n" );
document.write( "         The hypotenuse is x+8 = 29 ft.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.    +  = 441 + 400 = 841 = .    ! Correct !\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );