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Mrs. Nally's swimming pool is 10 feet by 6 feet. She paves the area around it with a sidewalk x feet wide, using 80 square feet of a new type of non-slip concrete. How wide is the sidewalk? A. The sidewalk is 20 feet wide. B. The sidewalk is 4 feet wide. C. The sidewalk is 10 feet wide. D. The sidewalk is 2 feet wide.

Respuesta :

Answer:

The sidewalk is 2 feet wide

Step-by-step explanation:

The area of the sidewalk is given as 80 square feet

The length and width of pool

including side walks will be;

10 + 2x and 6 + 2x

To get the area of the side walk

That will be area of total minus area of the pool

That will be ;

(10 + 2x)(6 + 2x) - 10(6) = 80

60 + 12x + 20x + 4x^2 - 60 = 80

4x^2 + 32x -80 = 0

x^2 + 8x -20

x^2 + 10x - 2x - 20 = 0

x(x + 10) -2(x + 10) = 0

(x-2)(x + 10) = 0

x = 2 or -10

since width cannot be negative;

The sidewalk is 2 feet wide

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