SOLUTION: Cynthia Besch wants to buy a rug for a room that is 11 ft. wide and 30 ft. long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 252 sq. ft. of

Question 460969: Cynthia Besch wants to buy a rug for a room that is 11 ft. wide and 30 ft. long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 252 sq. ft. of carpeting. What dimensions should the rug have?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Cynthia Besch wants to buy a rug for a room that is 11 ft. wide and 30 ft. long.
She wants to leave a uniform strip of floor around the rug. She can afford to buy 252 sq. ft. of carpeting.
What dimensions should the rug have?
:
Let x = the width of the uniform strip around the rug
then the rug dimensions will be: {11-2x) by (30-2x)
:
The rug area equation
{11-2x)*(30-2x) = 252
:
FOIL
330 - 22x - 60x + 4x^2 = 252
:
A quadratic equation
4x^2 - 82x + 330 - 252 = 0
4x^2 - 82x + 78 = 0
:
Simplify, divide by 2
2x^2 - 41x + 39 = 0
:
This will factor to
(2x - 39)(x - 1) = 0
only one solution will make sense
x = 1 ft is the uniform width around the rug
:
then the rug dimensions are:
11 - 2(1) = 9 ft
30 - 2(1) = 28 ft
:
:
Check this by finding the area of the rug with these dimensions;
9 * 28 = 252; confirms our solution
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