document.write( "Question 1131888: The length of a rectangle is 7 feet more than its width. The diagonal of the rectangle is 13 feet. Find the dimensions of the rectangle. \n" ); document.write( "

Algebra.Com's Answer #748606 by joshuajz(12) $\"\"$ $\"About$

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The first thing I'd do is create a drawing.
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\n" ); document.write( "Next you need to know the equation of the diagonal of a shape (The Pythagorean theorem):
\n" ); document.write( " $\"d%5E2+=+w%5E2+%2B+h%5E2\"$
\n" ); document.write( "Meaning we can now write an equation to solve for x
\n" ); document.write( " $\"%28x%5E2+%2B+%28x%2B7%29%5E2%29+=+13%5E2\"$
\n" ); document.write( " $\"%28x%5E2+%2B+x%5E2+%2B+14x+%2B+49%29+=+169\"$
\n" ); document.write( " $\"2x%5E2+%2B+14x+-+120+=+0\"$
\n" ); document.write( "Since this is in standard form and equal to 0 we can use the quadratic formula: $\"%28-b%2B-+sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29\"$
\n" ); document.write( " $\"%28-14%2B-+sqrt%2814%5E2-4%2A2%2A-120%29%29%2F%282%2A2%29\"$
\n" ); document.write( "Therefore:
\n" ); document.write( " $\"x+=+-+12\"$ OR $\"x+=+5\"$
\n" ); document.write( "Since a side length cannot be negative, we can \"Throw away\" the $\"x+=+-12\"$
\n" ); document.write( "Therefore: x = 5
\n" ); document.write( "Meaning the dimensions of the rectangle are 5 x 12
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