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The Pool Company installs custom-built swimming pools. One of its customers would like a rectangular pool with a sidewalk of equal width around the entire perimeter. To fit in the backyard, the pool and sidewalk together will have to be 1818 feet by 3636 feet.\newlineThe area of the pool in square feet can be modeled by the expression (18−2x)(36−2x)(18 - 2x)(36 - 2x), where xx is the width of the sidewalk in feet.\newlineWhat does the quantity 36−2x36 - 2x represent in the expression?\newlineChoices:\newline(A)the perimeter around the outside of the pool in feet\newline(B)the area of the pool in square feet\newline(C)the area of the sidewalk in square feet\newline(D)the length of the pool in feet

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Q. The Pool Company installs custom-built swimming pools. One of its customers would like a rectangular pool with a sidewalk of equal width around the entire perimeter. To fit in the backyard, the pool and sidewalk together will have to be 1818 feet by 3636 feet.\newlineThe area of the pool in square feet can be modeled by the expression (18−2x)(36−2x)(18 - 2x)(36 - 2x), where xx is the width of the sidewalk in feet.\newlineWhat does the quantity 36−2x36 - 2x represent in the expression?\newlineChoices:\newline(A)the perimeter around the outside of the pool in feet\newline(B)the area of the pool in square feet\newline(C)the area of the sidewalk in square feet\newline(D)the length of the pool in feet
  1. Identify Area Expression: The expression for the area of the pool is (18−2x)(36−2x)(18 - 2x)(36 - 2x). We need to identify what 36−2x36 - 2x represents.
  2. Dimensions of Pool and Sidewalk: The dimensions of the pool and sidewalk together are 1818 feet by 3636 feet. The width of the sidewalk is xx feet on all sides.
  3. Find Pool Length: To find the length of just the pool, we subtract the sidewalk's width from both sides of the total length, which is 3636 feet. So we do 36−x−x36 - x - x or 36−2x36 - 2x.
  4. Length of Pool Representation: Therefore, 36−2x36 - 2x represents the length of the pool in feet, not the perimeter or the area of the pool or sidewalk.

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