document.write( "Question 752687: Find the dimensions of a rectangle whose area is 216 cm2 and whose perimeter is 60 cm \n" ); document.write( "

Algebra.Com's Answer #457961 by MathLover1(20850) $\"\"$ $\"About$

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given:\r
\n" ); document.write( "\n" ); document.write( "area is $\"A=216cm%5E2\"$ and \r
\n" ); document.write( "\n" ); document.write( "perimeter is $\"P=60cm\"$ \r
\n" ); document.write( "\n" ); document.write( "if the length is $\"L\"$ and the width is $\"W\"$ , then\r
\n" ); document.write( "\n" ); document.write( " $\"L%2AW=216cm%5E2\"$ ......eq.1 and\r
\n" ); document.write( "\n" ); document.write( " $\"2%28L%2BW%29=60cm\"$ .....eq.2
\n" ); document.write( "__________________________\r
\n" ); document.write( "\n" ); document.write( "start with $\"2%28L%2BW%29=60cm\"$ .....eq.2 and solve for $\"L\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"L%2BW=60cm%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"L%2BW=30cm\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"L=30cm-W\"$ .....plug it in eq. 1 and solve for $\"W\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%2830cm-W%29b=216cm%5E2\"$ ......eq.1\r
\n" ); document.write( "\n" ); document.write( " $\"30%2AWcm-W%5E2=216cm%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=W%5E2-30%2AWcm%2B216cm%5E2\"$ or\r
\n" ); document.write( "\n" ); document.write( " $\"W%5E2-30%2AWcm%2B216cm%5E2=0\"$ ....use quadratic formula\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"W+=+%28-%28-30%29+%2B-+sqrt%28+%28-30%29%5E2-4%2A1%2A216+%29%29%2F%282%2A1%29+\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"W+=+%2830+%2B-+sqrt%28900-864+%29%29%2F2+\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"W+=+%2830+%2B-+sqrt%2836+%29%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"W+=+%2830+%2B-+6+%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( "solutions;\r
\n" ); document.write( "\n" ); document.write( " $\"W+=+%2830+%2B6+%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"W+=+36%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"W+=+18cm+\"$ \r
\n" ); document.write( "\n" ); document.write( "or\r
\n" ); document.write( "\n" ); document.write( " $\"W+=+%2830+-6+%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"W+=+24%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"W+=+12cm+\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "now find $\"L\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"L=30cm-W\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"W+=+18+cm\"$ => $\"L=30cm-18cm\"$ => $\"L=12cm\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"W+=+12cm+\"$ => $\"L=30cm-12cm\"$ => $\"L=18cm\"$ \r
\n" ); document.write( "\n" ); document.write( "since the length is usually greater we will say that $\"L=18cm\"$ and $\"W+=+12cm+\"$ \r
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