Final answer:
The dimensions of the rug Cynthia can afford, which are 17 ft by 25 ft, provide an area of 425 square feet, leaving a uniform strip of floor around the rug in the room.
Step-by-step explanation:
The question involves finding the dimensions of a rug that Cynthia Besch can afford, given that she wants to leave a uniform strip of floor around it in a room that is 19 ft by 27 ft, and she can buy only 425 square feet of carpeting. To solve this problem, the area of the rug needs to be calculated first. Since we know the area of carpeting she can buy, we can set up an equation where the product of the dimensions of the rug (length x width) equals 425 square feet. These dimensions should be less than those of the room since she wants a strip of floor around the rug.
Out of the options given:
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- 15 ft × 23 ft = 345 sq ft
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- 17 ft × 25 ft = 425 sq ft
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- 18 ft × 26 ft = 468 sq ft
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- 20 ft × 28 ft = 560 sq ft
Only the dimensions 17 ft by 25 ft result in an area of 425 sq ft, which is what she can afford. Therefore, the correct choice is option b. 17 ft x 25 ft.