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You are going to have a swimming pool put your back yard this summer. The dimensions of the pool are going to be 15 ft by 30 ft. There is going to be a concrete walkway around the outside of the pool, but they are not sure how wide it will be. The design of the pool, including the walkway, is shown below.

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MrRoyal

The perimeter of a shape is the sum of the all visible side lengths of the shape. The perimeter of the pool including the walkway is 90 + 8x

Given that:

[tex]Length = 15[/tex]

[tex]Width = 30[/tex]

Let the width of the walkway be x.

The dimension of the pool including the walkway is calculated by adding the dimension of the pool to the width of the walkway (on both sides):

So, we have:

[tex]Length = 15 + x + x[/tex]

[tex]Length = 15 + 2x[/tex]

[tex]Width = 30 + x + x[/tex]

[tex]Width = 30 + 2x[/tex]

The perimeter (P) of the walkway is then calculated using:

[tex]P = 2 \times (Length + Width)[/tex]

This gives:

[tex]P = 2 \times (15 + 2x + 30 + 2x)[/tex]

Collect like terms

[tex]P = 2 \times (15 + 30+ 2x + 2x)[/tex]

[tex]P = 2 \times (45+ 4x)[/tex]

Open brackets

[tex]P = 2 \times 45+ 2 \times 4x[/tex]

[tex]P = 90+ 8x[/tex]

Hence, the perimeter of the pool including the walkway is 90 + 8x (see attachment)

Read more about perimeters at:

https://brainly.com/question/6465134

Ver imagen MrRoyal

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