SOLUTION: The length of the rectangle is one more than the width. If the dimensions are both decreased by 2 units, the area of the new rectangle is 30 sq. units less than the area of the ori

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Question 811951: The length of the rectangle is one more than the width. If the dimensions are both decreased by 2 units, the area of the new rectangle is 30 sq. units less than the area of the original rectangle. Find the area of the original rectangle.
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
The equation for the area of a rectangle is: A+=+L%2AW
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Equation 1: L+=+1+%2B+W
Equation 2: L%2AW+=+%28L-1%29%2A%28W-1%29+%2B+30
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Since we know that L = (1+W), plug (1+W) into equation 2 for L.
Equation 2: L%2AW+=+%28L-1%29%2A%28W-1%29+%2B+30
%281%2BW%29%2AW+=+%28%281%2BW%29-1%29%2A%28W-1%29+%2B+30
Simplify
W+%2B+W%5E2+=+%28W%29%2A%28W-1%29+%2B+30
Multiply the W through.
W+%2B+W%5E2+=+W%5E2+-+W+%2B+30
Subtract W%5E2 from both sides.
W+=+-W+%2B+30
Add W to both sides.
2W+=+30
Divide both sides by 2
highlight%28W+=+15%29
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Now plug 15 into equation 1 for W.
Equation 1: L+=+1+%2B+W
L+=+1+%2B+%2815%29
highlight_green%28L+=+16%29
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Now find the original area by useing the equation A+=+L%2AW
A+=+%2816%29+%2A+%2815%29
highlight%28A+=+240%29
The area of the original rectangle is 240 square units.