document.write( "Question 568677: the length of a rectangular frame is 9 cm more than the width. the area inside the frame is 90 square cm. find the width of the frame. set up a quadratic equation to solve it. THANKS in advance \n" ); document.write( "

Algebra.Com's Answer #367119 by KMST(5328) $\"\"$ $\"About$

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Let the width be $\"x\"$ cm.
\n" ); document.write( "The length (in cm) is $\"x%2B9\"$ .
\n" ); document.write( "The area of the rectangle is length time width. In square centimeters, it's
\n" ); document.write( " $\"x%28x%2B9%29=x%5E2%2B9x\"$
\n" ); document.write( "If that is 90 square centimeters,
\n" ); document.write( " $\"x%5E2%2B9x=90\"$
\n" ); document.write( "The expected quadratic equation answer is probably $\"highlight%28x%5E2%2B9x-90=0%29\"$ , although $\"x%5E2%2B9x=90\"$ and $\"x%28x%2B9%29=90\"$ are equivalent equations.
\n" ); document.write( "To solve it, you could factor, complete the square, or use the quadratic formula.
\n" ); document.write( "Factoring, we see that $\"x%5E2%2B9x-90=%28x%2B15%29%28x-6%29\"$ so the equation transforms into
\n" ); document.write( " $\"%28x%2B15%29%28x-6%29=0\"$ with solutions $\"x=6\"$ and $\"x=-15\"$ .
\n" ); document.write( "Since the width of a frame is measured as a positive number, the only solution to the problem is
\n" ); document.write( " $\"highlight%28x=6%29\"$ .
\n" ); document.write( "The width of the frame is 6 cm. The length is 15 cm ( $\"6%2B9=15\"$ ). \n" ); document.write( "

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