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 increas

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Question 1127965: 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 josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!

Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~ 


The condition says


(8+x)*(12+x) - 8*12 = 69.


FOIL


8*12 + 12x + 8x + x^2 - 8*12 = 69


x^2 + 20x - 69 = 0


Factor left side polynomial


(x + 23)*(x-3) = 0.


The only positive root x= 3 works.


Answer.  The sides increased by 3 inches.


Check.   (8+3)*(12+3) - 8*12 = 69.     ! Correct !

Solved.


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