Question

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?
Length 2x
Width: x
Deck side width 4x

Answer 1

Let x = pool width. Pool length = 2x and the deck is 4x wide all around, so the overall outer dimensions are
length = 2x + 2(4x) = 10x,
width = x + 2(4x) = 9x.

a) Total area (pool + deck): A(x) = (10x)(9x) = 90x^2 (sq ft).
Pool area alone: Apool(x) = (2x)(x) = 2x^2 (sq ft).

b) If the pool width is 17 ft (x = 17), total area needed:
A(17) = 90(17^2) = 90(289) = 26,010 sq ft.

(For reference: pool area = 2(17^2) = 578 sq ft, so deck area = 26,010 − 578 = 25,432 sq ft.)