Question 1204421
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Cynthia Besch wants to buy a rug for a room that is 27ft wide and 35ft long. 
She wants to leave a uniform strip of floor around the rug. 
She can afford to buy 609 square feet of carpeting. What dimensions should the rug​ have?
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Let x be an unknown uniform width of the strip around the rug.


Then the dimensions of the rug are (27-2x) ft and (35-2x) ft.

The area equation is

    (27-2x)*(35-2x) = 609 sq. ft, the affordable area.


Simplify and find x

    27*35 - 70x - 54x + 4x^2 = 609

    4x^2 - 124x + 336 = 0

     x^2 - 31x + 84 = 0


Solve using the quadratic formula

    {{{x[1,2]}}} = {{{(31 +- sqrt(31^2 - 4*84))/2}}} = {{{(31 +- 25)/2}}}

    {{{x[1]}}} = {{{(31 + 25)/2}}} = 28;  {{{x[2]}}} = {{{(31 - 25)/2}}} = 3.


First root  {{{x[1]}}} = 28 ft is too large value, and we deny it;  second root {{{x[2]}}} = 3 is good: we accept it.


<U>ANSWER</U>.  The dimensions of the rug should be  27-2*3 = 21 ft  and  35-2*3 = 29 ft.
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Solved.