SOLUTION: The area of a carpet is 144 sq. meter. If its length is 2m less and its width is 5m more, the carpet will be a square. Find the dimension of the carpet. Show your work.

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Question 1173860: The area of a carpet is 144 sq. meter. If its length is 2m less and its width is 5m more, the carpet will be a square. Find the dimension of the carpet. Show your work.
Answer by ikleyn(52780) About Me  (Show Source):
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The area of a carpet is 144 sq. meter. If its length is 2m less and its width is 5m more, the carpet will be a square.
Find the dimension of the carpet.
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Let x be the measure of the square side, in meters.


Then the real dimensions of the carpet are (x+2) m  for the length and (x-5) m  for the width,
according to the condition.


The area equation is


    (x+2)*(x-5) = 144.


Simplify

    x^2 - 3x - 10 = 144

    x^2 - 3x - 154 = 0


    x%5B1%2C2%5D = %283+%2B-+sqrt%283%5E2+%2B+4%2A154%29%29%2F2 = %283+%2B-+sqrt%28625%29%29%2F2 = %283+%2B-+25%29%2F2.


It has two roots  14  and  -11.  Of them, only the value x= 14 is acceptable solution.


ANSWER.  The dimensions of the carpet are  14+2 = 16 m (the length)  and  14-5 = 9 m (the width).


CHECK.   a)  The area of the carpet is  16*9 = 144 square meters.       ! correct !

         b)  16 - 2 = 14;  9 + 5 = 14,  so  16-2 and 9+5 are equal sides of the square.    ! correct !

Solved.