Question

a swimming pool is shaped like a square. the distance between each of the pools corners is 20 feet. a pool cover with dimensions of 15 feet by 30 feet is used to protect the pool during the winter season. will the cover protect the entire pool? explain. select the correct choice below. a. no, because the pool cover is longer than the pool. b. no, because the pool cover is not as wide as the pool. c. yes, because the area of the pool cover is greater than the area of the pool.

Explanation:

Step1: Find pool side length

For a square with diagonal $d=20$ ft, side $s = \frac{d}{\sqrt{2}} = \frac{20}{\sqrt{2}} = 10\sqrt{2} \approx 14.14$ ft.

Step2: Compare cover to pool

The pool cover is 15 ft × 30 ft. The pool's side (~14.14 ft) is less than 15 ft, so the cover is wider and longer than the pool. The area of the pool is $s^2=(10\sqrt{2})^2=200$ sq ft, and the cover area is $15×30=450$ sq ft, which is larger, but the key is the cover's dimensions are sufficient to cover the square pool.

Step3: Evaluate options

Option C is correct because the cover's area is greater, and its dimensions are large enough to cover the pool.

Answer:

C. Yes, because the area of the pool cover is greater than the area of the pool.