document.write( "Question 165185: 37.) Show a complete solution to the problem.\r
\n" ); document.write( "\n" ); document.write( "If the perimeter of a rectangle is 20 feet and the diagonal is 2 squrt(13) feet then what are the length and width? \n" ); document.write( "

Algebra.Com's Answer #121837 by Alan3354(69443) $\"\"$ $\"About$

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37.) Show a complete solution to the problem.
\n" ); document.write( "If the perimeter of a rectangle is 20 feet and the diagonal is 2 squrt(13) feet then what are the length and width?
\n" ); document.write( "--------------------------
\n" ); document.write( "Perimeter = 2L + 2W = 20
\n" ); document.write( "Area = L*W
\n" ); document.write( " $\"D+=+SQRT%28L%5E2+%2B+W%5E2%29\"$ = $\"2sqrt%2813%29\"$
\n" ); document.write( "2L + 2W = 20
\n" ); document.write( "L + W = 10
\n" ); document.write( "W = 10-L
\n" ); document.write( "Sub into the other eqn
\n" ); document.write( " $\"sqrt%28L%5E2+%2B%2810-L%29%5E2%29+=+2sqrt%2813%29\"$
\n" ); document.write( "Square both sides
\n" ); document.write( "L^2 + (10-L)^2 = 4*13
\n" ); document.write( " $\"L%5E2+%2B+L%5E2+-+20L+%2B+100+=+52\"$
\n" ); document.write( " $\"2L%5E2+-+20L+%2B+48+=+0\"$
\n" ); document.write( " $\"L%5E2+-+10L+%2B+24+=+0\"$
\n" ); document.write( "(L-6)*(L-4)=0
\n" ); document.write( "L = 6, L= 4
\n" ); document.write( "If L=6, W=4
\n" ); document.write( "If L=4, W=6\r
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