SOLUTION: Cynthia Besch wants to buy a rug for a room that is 23 ft wide and 32 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 442 square feet of

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Cynthia Besch wants to buy a rug for a room that is 23 ft wide and 32 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 442 square feet of       Log On


   

Question 1137363: Cynthia Besch wants to buy a rug for a room that is 23 ft wide and 32 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 442 square feet of carpeting. What dimensions should the rug​ have?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Room area, 23*32
Rug area, (23-2x)(32-2x)
Uniform strip around rug, x
Rug area value will be 442 square feet.

highlight%28%2823-2x%29%2832-2x%29=442%29-------

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Algebra steps lead to 2x%5E2-55x%2B147=0.
.
discriminant is 43%5E2.

x=%2855%2B-+43%29%2F4

x=%2855-43%29%2F4
highlight_green%28x=3%29--------the uniform width between walls and rug

Rug Dimensions:
17 feet and 26 feet