Question

A company offers rectangular pool sizes with dimensions as shown. Each pool includes a deck around it.
a. Write a quadratic function to represent the area of the pool and the deck.
b. If Carolina wants a 17-ft wide pool with a​ deck, how many square feet will she need to have available in her​ yard?
Height of top layer: 4x
Length: 2x
Width: x

Answer 1

First write expressions in terms of x.

- Pool (inner) dimensions: length = 2x, width = x, so pool area P(x) = (2x)(x) = 2x^2.
- If the deck around the pool has width x on all sides, the outer (pool+deck) dimensions are
outer length = 2x + 2x = 4x and outer width = x + 2x = 3x,
so total area A(x) = (4x)(3x) = 12x^2.
- Deck area alone = A(x) − P(x) = 12x^2 − 2x^2 = 10x^2.

Now the numeric part depends on what “17‑ft wide” means:

1) If “17‑ft wide” means the pool’s width (the inner width x = 17 ft):
- x = 17, total area = 12(17^2) = 12·289 = 3,468 ft².

2) If “17‑ft wide” means the overall width including the deck (outer width = 3x = 17 ft):
- x = 17/3 ft, total area = 12(17/3)^2 = 12·289/9 = (4/3)·289 = 1,156/3 ≈ 385.33 ft².

Which interpretation did you intend?