SOLUTION: a rectangular pool is 10m by 3m on the floor.if the area is to be doubled by increasing the length and width by the same amount what is the new length and width

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Question 1125544: a rectangular pool is 10m by 3m on the floor.if the area is to be doubled by increasing the length and width by the same amount what is the new length and width
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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Let "w" be the increase of the length and the width.


Then our governing equation is


    (10+x)*(3+x) = 2*10*3 = 60.


One way is to solve it as a quadratic equation.


I will choose another way.


My task is to find a decomposition of the number 60 into the product of two factors, that differ in  10-3 = 7 units.


As soon as you reformulate the problem in this way, it is a matter of seconds to guess the answer. It is


    60 = 12*5.


So,  the new dimensions of the pool are 12 meters and 5 meters.


Check.  12*5 = 60 = 2*30;   12-10 = 2 = 5-3.

Solved.