Answer choices:
A. None
B. One
C. Two
D. Infinitely many

W = 4.646 ft

L = 9.292 ft

H = 3.097 ft

Step-by-step explanation:

Let's say the L is the length, W is the width, and H is the height.

The volume of the pool is:

V = LWH

The area of the pool is:

A = LW + 2LH + 2WH

L = 2W, so substituting:

V = (2W)WH

V = 2W²H

A = (2W)W + 2(2W)H + 2WH

A = 2W² + 4WH + 2WH

A = 2W² + 6WH

Solving for H in the first equation and substituting into the second:

H = V/(2W²)

A = 2W² + 3V/W

Find dA/dW and set to 0.

dA/dW = 4W − 3V/W²

0 = 4W − 3V/W²

4W = 3V/W²

4W³ = 3V

W = ∛(¾V)

V = 1000 gallons or 133.7 ft³.

W = ∛(¾(133.7 ft³))

W = 4.646 ft

So L = 9.292 ft and H = 3.097 ft.