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If the width of a rectangle is increased by 2 inches, the area is 140 square inches. If the legnth is increased by 1 inch, the area is 120 inches. Find the dimensions of the rectangle.

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From the description above, we know that:

(W+2) x L = 140
(L+1) x W = 120

where W = the width and L is the length, so...

WL + 2L = 140
WL + W = 120

Subtract the second equation from the first, you get...

2L - W = 20, so
W = 2L - 20.

So feed that back into the first of the original two equations:

(2L - 18) x L = 140

2L² - 18L - 140 = 0
so L² - 9L - 70 = 0
factorize it: (L - 14)(L + 5) = 0

so L = 14 or L = -5. The latter is impossible, so L = 14.
But W = 2L - 20, so W = 8.

Check it:

(W+2) x L = 10 x 14 = 140 Correct.
(L+1) x W = 15 x 8 = 120 Correct.

Answer: W = 8; L = 14.

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