SOLUTION: the length of a rectangle is 7 feet more than width. if the length were decreased by 3 feet and the width were increased by 2 feet, the perimeter would be 32 feet. Find the length

Question 126609: the length of a rectangle is 7 feet more than width. if the length were decreased by 3 feet and the width were increased by 2 feet, the perimeter would be 32 feet. Find the length of the original rectangle.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The length of the original rectangle is L, and the width is W. We also know that .

If we decrease the length by 3 we get , and if we increase the width by 2, we get .

The perimeter of a rectangle is given by , but we only know the perimeter of the new rectangle, so we have to use . But while we're at it, let's substitute for L so that we have a single equation in a single unknown.

Now collect terms and solve:

Since W is 5, L must be 5 + 7 = 12.

Check:
If we decrese the length by 3, we get 9, and if we increase the width by 2 we get 7. (2 * 9) + (2 * 7) = 18 + 14 = 32. Answer checks.
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