document.write( "Question 170758This question is from textbook
\n" ); document.write( ": The longer leg of a right triangle is 4 cm more than four times the length of the shorter leg. The hypotenuse is 1 cm longer than the longer leg. How long are the sides of the triangle? \n" ); document.write( "
Algebra.Com's Answer #126074 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
The longer leg of a right triangle is 4 cm more than four times the length of the shorter leg. The hypotenuse is 1 cm longer than the longer leg. How long are the sides of the triangle?
\n" ); document.write( ".
\n" ); document.write( "Let x = length of shorter leg
\n" ); document.write( "then
\n" ); document.write( "4x+4 = length of longer leg
\n" ); document.write( "4x+5 = length of hypotenuse
\n" ); document.write( ".
\n" ); document.write( "x^2 + (4x+4)^2 = (4x+5)^2
\n" ); document.write( "x^2 + (4x+4)(4x+4) = (4x+5)(4x+5)
\n" ); document.write( "x^2 + 16x^2+32x+16 = 16x^2+40x+25
\n" ); document.write( "17x^2+32x+16 = 16x^2+40x+25
\n" ); document.write( "x^2+32x+16 = 40x+25
\n" ); document.write( "x^2-8x+16 = 25
\n" ); document.write( "x^2-8x-9 = 0
\n" ); document.write( "(x-9)(x+1) = 0
\n" ); document.write( ".
\n" ); document.write( "x = {9, -1}
\n" ); document.write( "We can toss out the negative solution leaving:
\n" ); document.write( "x = 9 cm (shorter leg)
\n" ); document.write( ".
\n" ); document.write( "Longer leg:
\n" ); document.write( "x+4 = 9+4 = 13 cm
\n" ); document.write( ".
\n" ); document.write( " \n" ); document.write( "
\n" );