Final answer:
To relate the perimeter of the pool to its dimensions, create the equation 100 = 2(x + 4) + 2x, where x is the side length of the neighbor's square pool. Solving for x gives us the neighbor's pool side as 23 feet, making the new pool dimensions 23 feet in width and 27 feet in length.
Step-by-step explanation:
To create an equation that relates the perimeter of the pool to its dimensions, we need to understand the properties of geometric shapes. Since your neighbor's pool is square, it means all the sides are equal. Let's assume the side length of your neighbor's pool is x feet. Since you want to increase only the length by 4 feet, your pool would become a rectangle with one side having a length of x + 4 feet and the other side remaining x feet.
The perimeter of a rectangle is calculated by adding together the lengths of all four sides. In our case, the perimeter P is twice the length plus twice the width, or P = 2(x + 4) + 2x. Given that the total perimeter of your pool is 100 feet, we can write the equation:
100 = 2(x + 4) + 2x
To solve for x, you would perform the following steps:
- Distribute the 2 on the left side of the equation: 100 = 2x + 8 + 2x.
- Combine like terms: 100 = 4x + 8.
- Subtract 8 from both sides: 92 = 4x.
- Finally, divide by 4 to find x: x = 23.
Thus, the side length of your neighbor's pool is 23 feet, making the dimensions of your new pool 23 feet in width and 27 feet in length.