document.write( "Question 860476: what are the dimensions of a rectangular room that has a perimeter of 48 m and a area of 128 m2 \n" ); document.write( "

Algebra.Com's Answer #518499 by KMST(5328) $\"\"$ $\"About$

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If the room measures $\"x\"$ meters by $\"y\"$ meters,
\n" ); document.write( "its perimeter (in meters) would be
\n" ); document.write( " $\"2%28x%2By%29=48\"$ ,
\n" ); document.write( "and its surface area (in square meters) would be
\n" ); document.write( " $\"x%2Ay=128\"$ .
\n" ); document.write( "
\n" ); document.write( " $\"2%28x%2By%29=48\"$ <---> $\"x%2By=48%2F2\"$ <---> $\"x%2By=24\"$
\n" ); document.write( "Since $\"128=2%5E7=16%2A8\"$ and $\"16%2B8=24\"$ ,
\n" ); document.write( "it is obvious that the room could be $\"highlight%2816%29\"$ meters long by $\"highlight%288%29\"$ meters wide.
\n" ); document.write( "
\n" ); document.write( "The teacher may expect that you solve $\"x%2By=24\"$ for $\"y\"$ ,
\n" ); document.write( " $\"x%2By=24\"$ <---> $\"y=24-x\"$ ,
\n" ); document.write( "and then substitute into $\"x%2Ay=128\"$ ,
\n" ); document.write( "to get a quadratic equation:
\n" ); document.write( " $\"x%2A%2824-x%29=128\"$ --> $\"24x-x%5E2=128\"$ --> $\"x%5E2-24x%2B128=0\"$
\n" ); document.write( "You can solve $\"x%5E2-24x%2B128=0\"$ to get the two solutions
\n" ); document.write( " $\"x=8\"$ --> $\"y=24-8=16\"$ ,
\n" ); document.write( "and
\n" ); document.write( " $\"x=16\"$ --> $\"y=24-16=8\"$ ,
\n" ); document.write( "which tell you that the dimensions of that rectangular room
\n" ); document.write( "are $\"highlight%2816%29\"$ meters (length) and $\"highlight%288%29\"$ meters (width).
\n" ); document.write( " \n" ); document.write( "

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