document.write( "Question 981402: One of the side of a rectangle is 3m shorter than the other one. Find the sides of the rectangle if we know that if we increase every side with 1m, the surface of the rectangle will be increase with 18 meter square. \n" ); document.write( "

Algebra.Com's Answer #602390 by macston(5194) $\"\"$ $\"About$

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\n" ); document.write( "L=length; W=width=L-3m
\n" ); document.write( "Area before increase=(L)(W)=(L)(L-3m)=L^2-3L
\n" ); document.write( "Area after increase=(L+1m)(L-3m+1m)=(L+1m)(L-2m)=L^2-L-2m
\n" ); document.write( ".
\n" ); document.write( "Area after increase-area before increase=18m^2
\n" ); document.write( " $\"%28L%5E2-L-2m%29-%28L%5E2-3L%29=18m%5E2\"$
\n" ); document.write( " $\"L%5E2-L-2m-L%5E2%2B3L=18m%5E2\"$
\n" ); document.write( " $\"2L-2m=18m%5E2\"$
\n" ); document.write( " $\"2L=20\"$
\n" ); document.write( " $\"L=10m\"$ The original length was 10 meters.
\n" ); document.write( ".
\n" ); document.write( " $\"W=L-3m\"$ = $\"10m-3m=7m\"$ The original width was 7 meters.
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\n" ); document.write( "CHECK:
\n" ); document.write( "Area after 1m increase-area before 1m increase=18m^2
\n" ); document.write( ".
\n" ); document.write( " $\"%28L%2B1m%29%28W%2B1m%29-%28L%29%28W%29=18m%5E2\"$
\n" ); document.write( ".
\n" ); document.write( " $\"%2810m%2B1m%29%287m%2B1m%29-%2810m%29%287m%29=18m%5E2\"$
\n" ); document.write( ".
\n" ); document.write( " $\"%2811m%29%288m%29-70m%5E2=18m%5E2\"$
\n" ); document.write( ".
\n" ); document.write( " $\"88m%5E2-70m%5E2=18m%5E2\"$
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\n" ); document.write( " $\"18m%5E2=18m%5E2\"$ \r
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