A rectangular swimming pool that is 12ft by 15 ft has a deck of uniform width built around it. If the area of the deck is 198 square feet, find its width.

(12 +2w)(15 + 2w)= 198 + 180

4w^2 + 54 w - 198 = 0
2w^2 + 27w -99 = 0
(2w + 33)(w - 3) = 0
w = 3 ft

Here from 2021, a decade and a half later

To find the width of the deck, we need to subtract the area of the swimming pool from the total area of the pool with the deck.

The area of the pool can be found by multiplying its length by its width:
Area of Pool = length * width = 12 ft * 15 ft = 180 square feet.

To find the width of the deck, we can subtract the area of the pool from the total area of the pool with the deck:
Width of Deck = Total Area of Pool with Deck - Area of Pool.

Total Area of Pool with Deck = Area of Pool + Area of Deck = 180 sq ft + 198 sq ft = 378 sq ft.

Thus, the width of the deck is:
Width of Deck = Total Area of Pool with Deck - Area of Pool = 378 sq ft - 180 sq ft = 198 sq ft.

Therefore, the width of the deck is 198 square feet.

To find the width of the deck, we need to subtract the area of the pool from the total area that includes the pool and deck.

First, let's find the area of the pool. The pool has dimensions 12ft by 15ft, so its area is given by the product of its length and width: 12ft * 15ft = 180 square feet.

The total area, including the pool and deck, is the area of the pool plus the area of the deck: 180 square feet + 198 square feet = 378 square feet.

Now, let's assume the width of the deck around the pool is "x" feet. Since the deck goes around all four sides of the pool, we can calculate the overall dimensions of the pool and deck combination as follows:

Length of pool and deck = length of pool + 2 * width of deck
Width of pool and deck = width of pool + 2 * width of deck

Substituting the given values and the unknown width of the deck (x), we have:

Length of pool and deck = 15ft + 2x
Width of pool and deck = 12ft + 2x

To find the width of the deck, we need to solve the equation:

Area of pool and deck = (length of pool and deck) * (width of pool and deck)

Substituting the calculated total area (378 square feet) and the corresponding expressions for length and width, we get:

378 square feet = (15ft + 2x) * (12ft + 2x)

Expanding this equation further, we have:

378 square feet = 180 square feet + 24ft * x + 30ft * x + 4 * x^2

Combining like terms, we get:

4 * x^2 + 54ft * x + 180 square feet - 378 square feet = 0

Simplifying the equation, we have:

4 * x^2 + 54ft * x - 198 square feet = 0

Now, we can solve this quadratic equation for x using factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 4, b = 54ft, and c = -198 square feet. Plugging in these values, we can calculate x:

x = (-(54ft) ± √((54ft)^2 - 4 * 4 * (-198 square feet))) / (2 * 4)

Simplifying further:

x = (-54ft ± √(2916ft^2 + 3168 square feet)) / 8

x = (-54ft ± √(8766ft^2)) / 8

x = (-54ft ± 93.6ft) / 8

This gives two possible solutions:

x = (-54ft + 93.6ft) / 8 ≈ 5.7ft (approximate value)

x = (-54ft - 93.6ft) / 8 ≈ -14.6ft (approximate value)

Since the width cannot be negative, the width of the deck is approximately 5.7 feet.