The length of a rectangular swimming pool is 15 feet longer than the width. If the perimeter is 82 feet, then what are the length and the width?

w = w

L = w+15
2 w + 2(w+15) = 82
4 w + 30 = 82
4 w = 52
w = 13
L = w+15 = 28

Let's denote the width of the pool as 'w'.

According to the given information, the length of the pool is 15 feet longer than the width, which means it can be represented as 'w + 15'.

The perimeter of a rectangle is given by the formula: Perimeter = 2 * (length + width).

Substituting the values into this formula:

82 = 2 * (w + w + 15)

Simplifying the equation:

82 = 2 * (2w + 15)

Now, let's solve for 'w':

82 = 4w + 30

Subtracting 30 from both sides of the equation:

52 = 4w

Dividing both sides by 4:

w = 13

So, the width of the pool is 13 feet.

Now, let's find the length:

Length = Width + 15

Length = 13 + 15

Length = 28

Therefore, the length of the pool is 28 feet and the width is 13 feet.

To find the length and width of the rectangular swimming pool, we can set up a system of equations based on the given information.

Let's assume that the width of the pool is "w" feet. Since the length is 15 feet longer than the width, the length can be represented as "w + 15" feet.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. For a rectangle, opposite sides are equal in length. So, the perimeter of the pool is given by:

Perimeter = 2(length + width)

We are given that the perimeter is 82 feet. Substituting the values, we can write the equation as:

82 = 2((w + 15) + w)

Let's solve this equation step by step.

First, we distribute the 2 to both terms inside the parentheses:
82 = 2w + 30 + 2w

Combining like terms:
82 = 4w + 30

Next, we isolate the variable on one side by subtracting 30 from both sides of the equation:
82 - 30 = 4w

Simplifying:
52 = 4w

To solve for "w", we divide both sides of the equation by 4:
52/4 = w

Simplifying:
13 = w

Therefore, the width of the swimming pool is 13 feet.

To find the length, substitute the value of the width back into the equation for the length:
Length = Width + 15
Length = 13 + 15
Length = 28

So, the length of the swimming pool is 28 feet, and the width is 13 feet.