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 1717​-ft wide pool with a​ deck, how many square feet will she need to have available in her​ yard?

Answer 1

I don't have the diagram or the algebraic expressions for the pool dimensions, so I can't write the specific quadratic yet. Could you confirm the pool length expression and the deck width from the picture? (For example, is the pool length given as something like 2x+5 and the deck width 3 ft?)

Meanwhile, here is the general method and the formula you can use:

- Let the pool width be w and the pool length be L (L may be given in terms of w or x in the diagram).
- Let the deck have uniform width d around the pool.
- The total width including the deck = w + 2d. The total length including the deck = L + 2d.
- So the total area (pool + deck) as a function of the variable (for example x or w) is
A = (w + 2d)(L + 2d).

If the diagram gives L as an expression in the same variable (for example L = 2w + 5), substitute that expression and expand to get a quadratic.

Example: if the pool width is 17 ft, the pool length is L = 2(17)+5 = 39 ft, and the deck width is d = 3 ft, then
- total dimensions = (17 + 6) by (39 + 6) = 23 by 45,
- total area = 23 × 45 = 1035 square feet.

If you post the exact expressions from the diagram (the length formula and the deck width), I will write the specific quadratic and compute the area for the 17‑ft wide pool.