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A swimming pool is to be constructed in a 1,408-ft2 backyard. There is to be a fence that will surround a 12-by-24-foot pool. The pool builder wants to build a concrete paver deck of a uniform width, x, surrounding the pool and filling the entire area of the backyard. What is the width of the pool deck?

9 ft
10 ft
11 ft
12 ft

Respuesta :

mhanifa

Answer:

  • B. 10 ft

Step-by-step explanation:

Let the width of the pool deck be x.

  • Dimensions of the pool are 12 + 2x and 24 + 2x.
  • Total area is 1408 ft².

We have equation:

  • (12 + 2x)(24 + 2x) = 1408
  • 12*24 + 12*2x + 24*2x + (2x)² = 1408
  • 288 + 72x + 4x² = 1408
  • 4x² + 72x + 288 - 1408 = 0
  • 4x² + 72x - 1120 = 0
  • x² + 18x - 280 = 0
  • x² - 10x + 28x - 280 = 0
  • x(x - 10) + 28(x - 10) = 0
  • (x - 10)(x + 28) = 0

1)

  • x - 10 = 0
  • x = 10

2)

  • x + 28 = 0
  • x = - 28 (discarded as negative)

Correct choice is B

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