document.write( "Question 1167042: a rectangle is drawn so the width is 9 inches longer than the height. If the rectangle's diagonal measurement is 45 inches, find the height \n" ); document.write( "

Algebra.Com's Answer #791612 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "H = height\r\n" );
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document.write( "length = H+9\r\n" );
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document.write( "Diagonal \r\n" );
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document.write( "    H^2 + (H+9)^2 = 45^2\r\n" );
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document.write( "    2H^2 + 18H + 81 = 2025\r\n" );
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document.write( "    2H^2 + 18H - 1944 = 0\r\n" );
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document.write( "     H^2 + 9H - 972 = 0\r\n" );
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document.write( "Factor\r\n" );
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document.write( "    (H-27)*(H+36) = 0\r\n" );
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document.write( "The roots are  H= 27  and  H= -36.\r\n" );
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document.write( "Only positive root works.\r\n" );
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document.write( "ANSWER.  The height is 27 inches.\r\n" );
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\n" ); document.write( "\n" ); document.write( "A post-solution notice\r
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document.write( "    This triangle is nothing else as a famous (3,4,5)-right angled triangle with the similarity factor of 9.\r\n" );
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