SOLUTION: A rectangle is 8 inches and 12 inches long. If the dimensions are increased by the same amount, thereby its area is increased by 69 square inches, by what amount is the side increa
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Question 1127813: A rectangle is 8 inches and 12 inches long. If the dimensions are increased by the same amount, thereby its area is increased by 69 square inches, by what amount is the side increased? Found 2 solutions by greenestamps, josgarithmetic:Answer by greenestamps(13200) (Show Source):
This is fairly easy to solve without formal algebra.
One dimension is 4 inches more than the other; when each dimension is increased by the same amount , the difference in the dimensions will still be 4 inches.
The original area is 96 square inches; the new area is 96+69 = 165 square inches.
Do some easy mental calculations to find two numbers whose difference is 4 and whose product is 165; the answer is 15 and 11.
So each dimension was increased by 3 inches.
If you need an algebraic solution, write and solve the equation that says the difference between 8*12 and (8+x)*(12+x) is 69:
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