SOLUTION: a rug measuring 9m by 12m was installed in a recreational hall. A strip of floor of equal width was left uncovered along all edges of the hall. the area of the uncovered floor is 2

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Question 1150376: a rug measuring 9m by 12m was installed in a recreational hall. A strip of floor of equal width was left uncovered along all edges of the hall. the area of the uncovered floor is 270m^2. how wide is the uncovered strip
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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The area of the uncovered floor = (9+2x)*(12+2x) - 9*12 = 4x^2 + 42x.


The equation to find the uniform strip width is


    4x^2 + 42x = 270  square meters,  or


    4x^2 + 42x - 270 = 0.


    x%5B1%2C2%5D = %28-42+%2B-+sqrt%28%28-42%29%5E2+%2B+4%2A4%2A270%29%29%2F%282%2A4%29 = %28-42+%2B-+78%29%2F8.


Only positive root  x = %28-42+%2B+78%29%2F8 = 4.5  makes sense.


ANSWER.  The uniform width of the strip is 4.5 meters.

Solved.

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Thanks to @MathTherapy (!)




Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

a rug measuring 9m by 12m was installed in a recreational hall. A strip of floor of equal width was left uncovered along all edges of the hall. the area of the uncovered floor is 270m^2. how wide is the uncovered strip
IKLEYN made a mistake. Her denominator should be 8 i/o 16.
Thus, the answer's actually highlight_green%28matrix%281%2C2%2C+4.5%2C+meters%29%29