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GuDViN [60]
1 year ago
13

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 pat

io would need to be removed in order to have a 1 foot walkway around the pool?
Mathematics
1 answer:
trasher [3.6K]1 year ago
7 0

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

<em>See attachment for illustration</em>

Read more about perimeters at:

brainly.com/question/6465134

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