document.write( "Question 1060532: The length of a rectangle is 10 feet longer than it is wide. If each side is increased 10 feet, then the area is multiplied by 2. What was the size of the original rectangle? \n" ); document.write( "

Algebra.Com's Answer #675463 by math_helper(2461) $\"\"$ $\"About$

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l = w+10 —> Area = lw = (w+10)w = $\"w%5E2+%2B+10w+\"$ (substituted w+10 for l)\r
\n" ); document.write( "\n" ); document.write( "The other relation given is:
\n" ); document.write( "(l+10)(w+10) = 2*Area\r
\n" ); document.write( "\n" ); document.write( "Again, substitute w+10 for l:
\n" ); document.write( " $\"+%28%28w%2B10%29+%2B+10%29+%28w%2B10%29+=+2%2AArea+\"$
\n" ); document.write( " $\"++%28w%2B20%29%28w%2B10%29+=+2%2AArea+\"$
\n" ); document.write( " $\"++w%5E2+%2B+30w+%2B+200+=+2%2AArea+\"$
\n" ); document.write( "—
\n" ); document.write( "2*Area is $\"+2%2A%28w%5E2%2B10w%29+\"$ or $\"+2w%5E2+%2B+20w+\"$
\n" ); document.write( "—
\n" ); document.write( "So $\"+w%5E2+%2B+30w+%2B+200+=+2w%5E2+%2B+20w+\"$
\n" ); document.write( " $\"+-w%5E2+%2B10w+%2B+200+=+0+\"$
\n" ); document.write( " $\"++w%5E2+-+10w+-+200+=+0+\"$
\n" ); document.write( " $\"++%28w-20%29%28w%2B10%29+=+0+\"$
\n" ); document.write( " $\"+w=20\"$ or $\"+w=-10\"$
\n" ); document.write( "Discard w=-10 because it makes no sense.\r
\n" ); document.write( "\n" ); document.write( "—
\n" ); document.write( "Ans: width is 20, length is 30
\n" ); document.write( "—\r
\n" ); document.write( "\n" ); document.write( "Check: Area = 20*30 = 600
\n" ); document.write( "and for the expanded rectangle:
\n" ); document.write( " (20+10)(30+10) = (30)(40) = 1200 = 2*Area \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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