SOLUTION: Cynthia Besch wants to buy a rug for a room that is 18 feet wide and 19 feet long. She wants to leave a uniform strip around the rug. She can afford 272 square feet of carpeting. W

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Question 992571: Cynthia Besch wants to buy a rug for a room that is 18 feet wide and 19 feet long. She wants to leave a uniform strip around the rug. She can afford 272 square feet of carpeting. What dimensions should the rug have?
272+(19-2x)(18+2x)
1, 35/2
But, what are the dimensions in feet? How do I convert? Thanks.
Found 2 solutions by rothauserc, vleith:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
The border will be inside the dimensions of the room, therefore
(19-2x) * (18-2x) = 272
342 - 74x + 4x^2 = 272
rearrange the terms
4x^2 - 74x + 342 = 272
divide both sides of = by 4
x^2 - 18.5x + 85.5 = 68
subtract 68 from both sides of =
x^2 - 18.5x + 17.5 = 0
use quadratic formula to solve for x
x = (-(-18.5) + sqrt((18.5^2)−(4×17.5))) / 2 = 17.5
x = (-(-18.5) - sqrt((18.5^2)−(4×17.5))) / 2 = 1
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The reasonable dimension for the strip around the rug is 1 foot, therefore
the dimensions for the rug are 17 feet long and 16 feet wide
Answer by vleith(2983)   (Show Source): You can put this solution on YOUR website!
Let the width of the strip be x
The rug will have square footage of (18-2x)*(19-2x)
you are told she wants a rug that is 272 sq ft
so


Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4356 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 17.5, 1. Here's your graph:


so the strip will be 1 ft wide
That makes the rug (18-2) by (19-2) feet
16 feet by 17 feet
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