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.
To find the width of the deck around the rectangular swimming pool, we need to subtract the area of the pool from the total area that includes the pool and the deck.
Let's start by finding the total area of the larger rectangle that includes both the pool and the deck.
The length of the larger rectangle would be the original length of the pool plus twice the width of the deck on each side. So, the length of the larger rectangle would be:
Length of larger rectangle = Length of pool + 2 * Width of deck
Similarly, the width of the larger rectangle would be the original width of the pool plus twice the width of the deck on each side. So, the width of the larger rectangle would be:
Width of larger rectangle = Width of pool + 2 * Width of deck
To find the area of the larger rectangle, we multiply its length by its width:
Area of larger rectangle = Length of larger rectangle * Width of larger rectangle
The area of the pool is given as 12 ft * 15 ft = 180 square feet.
Now, let's set up an equation to find the width of the deck:
Area of the deck = Area of larger rectangle - Area of pool
198 sq ft = (Length of larger rectangle * Width of larger rectangle) - 180 sq ft
Since we already know the dimensions of the pool (12 ft by 15 ft), we can substitute these values in the equation:
198 sq ft = ((12 ft + 2 * Width of deck) * (15 ft + 2 * Width of deck)) - 180 sq ft
Now, we can solve this equation to find the width of the deck.