Answer: the width of the deck is 18 feet
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