document.write( "Question 1042388: A rectangle is drawn so the width is 97 inches longer than the height. If the rectangle's diagonal measurement is 113 inches, find the height. \n" ); document.write( "
Algebra.Com's Answer #657361 by ankor@dixie-net.com(22740)\"\" \"About 
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A rectangle is drawn so the width is 97 inches longer than the height.
\n" ); document.write( "x = the height
\n" ); document.write( "the
\n" ); document.write( "(x+97) = the width
\n" ); document.write( " If the rectangle's diagonal measurement is 113 inches, find the height.
\n" ); document.write( "The diagonal is the hypotenuse, use Pythagoras to find the height
\n" ); document.write( "x^2 + (x+97)^2 = 113^2
\n" ); document.write( "x^2 + x^2 + 194x + 9409 = 12769
\n" ); document.write( "2x^2 + 194x + 9409 - 12769 = 0
\n" ); document.write( "2x^2 + 194x - 3360 = 0
\n" ); document.write( "simplify divide by 2
\n" ); document.write( "x^2 + 97x - 1680 = 0
\n" ); document.write( "You can use the quadratic formula a=1; b=97; c=-1680, but this will factor to
\n" ); document.write( "(x+112)(x-15) = 0
\n" ); document.write( "The positive solution is what we want here
\n" ); document.write( "x = 15 inches is the height
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\n" ); document.write( "See if that checks out, the width: 15+97 = 112, find the hypotenuse with these values
\n" ); document.write( "h = \"sqrt%2815%5E2+%2B+112%5E2%29\" in your calc
\n" ); document.write( "h = 113 \n" ); document.write( "
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