Question 1195712
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Cynthia Besch wants to buy a rug for a room that is 21ft wide and 28ft long. 
She wants to leave a uniform strip of floor around the rug. 
She can afford to buy 494 square feet of carpeting. 
What dimensions should the rug​ have?
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<pre>
Let "x" be the uniform width of the strip. 

Then the dimensions of the rug are (21-2x) and (28-2x). 

Thus the area of the rug is (21-2x)*(28-2x).


According to the condition, it must be equal to 494.  It gives you an equation

(21-2x)*(28-2x) = 494


{{{588 - 42x - 56x + 4x^2}}} = 494

{{{4x^2 - 98x + 94}}} = 0

{{{2x^2 - 49x + 47}}} = 0

The discriminant   d = {{{49^2 - 4*2*47}}} = 2025.

{{{x[1,2]}}} = {{{(49 +- sqrt(2025))/(2*2)}}} = {{{(49 +- 45)/4}}}.


There are two roots.


{{{x[1]}}} = {{{(49 + 45)/4}}} = 23.5  is, obviously, too big (more than the wide of the room) 
                                       and, therefore, does not work as the solution to the problem.


{{{x[2]}}} = {{{(49-45)/4}}} = 1  perfectly suits as the solution.


<U>Check</U>.  (21-2*1)*(28-2*1) = 19*26 = 494,  the area of the rug


<U>Answer</U>.  The rug should be 19 by 26 feet.
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Solved.