SOLUTION: a rectangle is three times as long as it is wide. if its length and width are both decreased by 2cm, its area is decreased by 36cm squared. find its original dimensions.

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Question 174027: a rectangle is three times as long as it is wide. if its length and width are both decreased by 2cm, its area is decreased by 36cm squared. find its original dimensions.
Answer by solver91311(24713) About Me  (Show Source):
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The width is w so the length is 3w. The area of the original rectangle is then 3w%5E2

The smaller rectangle measures w-2 by 3w-2, and the new area is 3w%5E2-8w-4, but this new area is 36cm%5E2 smaller than the original, so

3w%5E2-8w-4=3w%5E2-36

Collect terms, solve for w and you have the original width.