SOLUTION: The are of a 12m by 8m rectangle is to be doubled. By what equal amount must each dimensions be increased?

Question 1097599: The are of a 12m by 8m rectangle is to be doubled. By what equal amount must each dimensions be increased?

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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1 - Mental solution

The original area = 12*8 = 96 sq. m.

The doubled area = 96*2 = 192 sq. m.


Now I should factor 192 into the product of two factors with the difference between them equal to 12-8 = 4:

192 = 96*2 = 48*4 = 24*8 = 12*16     (!)  Ops (!!!)


Answer. The new dimensions are 16 and 12, and the increase of each dimension is 4 m.

2 - Algebra solution

(12+x)*(8+x) = 2*12*8,   or

x^2 + 40x - 96 = 0,

(x+36)*(x-4) = 0,


and the only positive root x= 4 is the solution to the problem.

Solved.

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