A rectangular pool is 30 feet wide and 40 feet long. It is surrounded on all four sides by a wooden deck that is x feet wide. The total area enclosed within the perimeter of the deck is 2784 square feet. What is the width of the deck?

Answer: the width of the deck is 18 feet

Step-by-step explanation:

Let x represent the width of the deck.

If rectangular pool is 30 feet wide, it means that the total width of the pool including the wooden deck is

(30 + x) feet

If rectangular pool is 40 feet long, it means that the total length of the pool including the wooden deck is

(40 + x) feet

The total area enclosed within the perimeter of the deck is 2784 square feet. This means that

(30 + x) (40 + x) = 2784

1200 + 30x + 40x + x² = 2784

x² + 70x + 1200 - 2784 = 0

x² + 70x - 1584 = 0

x² + 88x - 18x - 1584 = 0

x (x + 88) - 18 (x + 88) = 0

x - 18 = 0 or x + 88 = 0

x = 18 or x = - 88

since the width cannot be negative, then x = 18