document.write( "Question 151724: The length of a rectangle is 7 meters more than the width. the length of a diagonal is 13 meters. find the length \n" ); document.write( "
Algebra.Com's Answer #111565 by mducky2(62)\"\" \"About 
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Although the problem gives you the information as if you were looking for the sides of a rectangle, the fact that it gives you the length of the diagonal means that you can treat the information as if it were about a right triangle. We can use the Pythagoream theorem:
\n" ); document.write( "a2 + b2 = c2
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However, we only know definitively the length of the diagonal. In order to solve a single equation, we can only have one variable.
\n" ); document.write( "width: w
\n" ); document.write( "length of the rectangle: w + 7
\n" ); document.write( "diagonal: 13
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Now we can set up the equation:
\n" ); document.write( "w2 + (w+7)2 = 132
\n" ); document.write( "w2 + w2 + 14w + 49 = 169
\n" ); document.write( "2w2 + 14w - 120 = 0
\n" ); document.write( "w2 + 7 w - 60 = 0
\n" ); document.write( "(w+12)(w-5) = 0
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\n" ); document.write( "There are two options. Either w+12 = 0 or w-5=0. However, only one of these will have a positive numbered answer.
\n" ); document.write( "w + 12 = 0
\n" ); document.write( "w = -12
\n" ); document.write( "This is wrong because the width can't be negative.
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w-5 = 0
\n" ); document.write( "w = 5
\n" ); document.write( "This must be the width.
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Now we can find the length of the rectangle:
\n" ); document.write( "length = w + 7
\n" ); document.write( "= 5 + 7
\n" ); document.write( "= 12
\n" ); document.write( "
Therefore, for this rectangle, the width is 5 meters and the length is 12 meters. \n" ); document.write( "
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