Question 1127965
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A rectangle is 8 inches {{{highlight(wide)}}} 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?
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<pre>
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.


<U>Answer</U>.  The sides increased by 3 inches.


<U>Check</U>.   (8+3)*(12+3) - 8*12 = 69.     ! Correct !
</pre>

Solved.