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A rectangular swimming pool is 20 feet by 28 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 884 square feet. What is the width of the deck?
A. 2 feet
B. 2.5 feet
C. 3 feet
D. 4 feet
E. 5 feet
Correct Answer: C
Explanation/Reference:
Explanation:
Since we are trying to find the width of the deck, let x = the width of the deck. Therefore, x + x + 20 or 2x + 20 is the width of the entire figure. In the same way, x + x + 28 or 2x + 28 is the length of the entire figure.
The area of a rectangle is length × width, so use A = l × w.
Substitute into the equation: 884 = (2x + 20)(2x + 28)
Multiply using FOIL: 884 = 4×2 + 56x + 40x + 560
Combine like terms: 884 = 4×2 + 96x + 560
Subtract 884 from both sides: 884 884 = 4×2 + 96x + 560 884 0 = 4×2 + 96x 324
Divide each term by 4: 0 = x2 + 24x 81
Factor the trinomial: 0 = (x + 27)(x 3)
Set each factor equal to zero and solve: x + 27 = 0 or x 3 = 0 x = 27 x = 3
Since we are solving for a length, the solution of 27 must be rejected. The width of the deck is 3 feet.
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