document.write( "Question 140787: The diagonal of a rectangle platform is square root of 20 cm. If both dimensions are increased by 2 cm, then the resulting perimeter would be 5/3 of the original perimeter. Find the dimensions of the rectangle. \n" ); document.write( "

Algebra.Com's Answer #102522 by Fombitz(32388) $\"\"$ $\"About$

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Let call the length and width of the rectangle L and W.
\n" ); document.write( "1. $\"L%5E2%2BW%5E2=20\"$
\n" ); document.write( "The original perimeter is 2L+2W.
\n" ); document.write( "2. $\"2%28L%2B2%29%2B2%28W%2B2%29=%285%2F3%29%282L%2B2W%29\"$
\n" ); document.write( "Simplifying 2 (multiply both sides by 3 to get rid of denominators),
\n" ); document.write( " $\"6%28L%2B2%29%2B6%28W%2B2%29=5%282L%2B2W%29\"$
\n" ); document.write( " $\"6L%2B12%2B6W%2B12=10L%2B10W\"$
\n" ); document.write( " $\"4L%2B4W=24\"$
\n" ); document.write( " $\"L%2BW=6\"$
\n" ); document.write( " $\"L=6-W\"$
\n" ); document.write( "Now plug this value into 1.
\n" ); document.write( "1. $\"L%5E2%2BW%5E2=20\"$
\n" ); document.write( " $\"%286-W%29%5E2%2BW%5E2=20\"$
\n" ); document.write( " $\"%2836-12W%2BW%5E2%29%2BW%5E2=20\"$
\n" ); document.write( " $\"2W%5E2-12W%2B36=20\"$
\n" ); document.write( " $\"2W%5E2-12W%2B16=0\"$
\n" ); document.write( " $\"W%5E2-6W%2B8=0\"$
\n" ); document.write( " $\"%28W-4%29%28W-2%29=0\"$
\n" ); document.write( "The two solutions are W=4 and W=2.
\n" ); document.write( "For W=4, L=6-W=2.
\n" ); document.write( "For W=2, L=6-W=4.
\n" ); document.write( "The dimensions of the rectangle are 2 cm by 4 cm.
\n" ); document.write( " \n" ); document.write( "

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