SOLUTION: Cynthia Besch wants to buy a rug for a room that is 26 ft wide and 34 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 384 square feet of

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Question 1123166: Cynthia Besch wants to buy a rug for a room that is 26 ft wide and 34 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 384 square feet of carpeting. What dimensions should the rug have?
Found 2 solutions by ankor@dixie-net.com, greenestamps:
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 26 ft wide and 34 ft long.
She wants to leave a uniform strip of floor around the rug.
She can afford to buy 384 square feet of carpeting.
What dimensions should the rug have?
:
let x = the width of the uniform strip around the rug
then the dimensions of the rug will be (34-2x) by (26-2x)
The equation
(34-2x) * (26-2x) = 384 sq/ft
FOIL
884 - 68x - 52x + 4x^2 = 384
Arrange as a quadratic equation
4x^2 - 120x + 884 - 384 = 0
4x^2 - 120x + 500 = 0
simplify, divide by 4
x^2 - 30x + 125 = 0
Factors easily to
(x-25)(x-5) = 0
only 1 solution makes sense
x = 5 ft is the width of the uniform strip around the rug
Find the dimensions of the rug
34 - 2(5) = 24 ft
26 - 2(5) = 16 ft
the rug should be 24 by 16 which has an area: 24*16 = 384

Answer by greenestamps(13195) (Show Source):
You can put this solution on YOUR website!

The room is 8 feet longer than it is wide. If the strip of floor around the rug is uniform, then the rug is also 8 feet longer than it is wide.

So let the width of the rug be x; then the length is x+8. And the area of the rug is to be 384:

or

Clearly the negative solution does not make sense in the actual problem. So the width is 16 feet, which means the length is 24 feet.