Question

Your family is installing a new square pool in the backyard. The existing patio has a side length of 8 feet. How much of the patio would need to be removed in order to have a 1 foot walkway around the pool?

Answer 1

The question is an illustration of perimeters.

The amount of patio to remove to install the pool is 8 feet.

From the question, we have:

$\mathbf{Length\ of\ the\ pool = 8}$

$\mathbf{Length\ of\ walkway = 1}$

The perimeter of the patio is:

$\mathbf{P_p = 4 \times Length\ of\ the\ pool}$

$\mathbf{P_p = 4 \times 8}$

$\mathbf{P_p = 32}$

A 1ft walkway means that;

1ft would be subtracted from both sides of the patio before installing the pool

So, the perimeter of the patio in terms of the length of the pool is:

$\mathbf{P_p = 4 \times (x +2)}$

Equate both expressions

$\mathbf{P_p = P_p}$

$\mathbf{4 \times (x +2) = 32}$

Divide both sides by 4

$\mathbf{x +2 = 8}$

Subtract 2 from both sides

$\mathbf{x = 6}$

So, the perimeter of the pool is:

$\mathbf{P_{pool} = 4 \times 6}$

$\mathbf{P_{pool} = 24}$

The amount of patio to remove is:

$\mathbf{Amount = P_p - P_{pool}}$

So, we have:

$\mathbf{Amount = 32 - 24}$

$\mathbf{Amount = 8}$

Hence, 8ft of the patio would be removed to install the pool

See attachment for illustration

Read more about perimeters at:

https://brainly.com/question/6465134