Cynthia Besch wants to buy a rug for a room that is 21 ft wide and 34 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 338 square feet of carpeting. What
dimensions should the rug have?

Dimensions of the rug = 13 ft × 26 ft

Step-by-step explanation:

Dimensions of the room = 21 ft × 34 ft

Area of the room = 21 × 34 = 714 ft²

Cynthia wants to leave a uniform strip of floor around the rug.

Let the width of the rug = x ft

Then the dimensions of the rug will be = (21- 2x)ft × (34 - 2x)ft

Area of the rug = (21 - 2x)×(34 - 2x) square feet

338 = (21 - 2x)×(34 - 2x)

338 = 714 - 68x - 42x + 4x²

4x² - 110x + 714 - 338 = 0

4x² - 110x + 376 = 0

2x² - 55x + 188 = 0

2x² - 47x - 8x + 188 = 0

x(2x - 47) - 8(x - 47) = 0  

(x - 4)(2x - 47) = 0

x = 4,

For x = 23.5 area of the rug will be negative.

Therefore, x = 4 ft will be the width of the rug.

Dimensions of the rug will be 13 ft × 26 ft. 

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