Chapter 11: Q8. (page 735)

Peggy is having a cement walkway installed around the perimeter of her swimming pool with the dimensions shown below. If $x = 3$ find the area, in square feet, of the pool and walkway.

Short Answer

Expert verified

The area of the pool is 180 ft² and the area of the walkway is 210 ft².

Step by step solution

Step 1. Define the area of the rectangle.

The area of the rectangle $=$ Length $\times$ Width ………… (1)

Step 2. Calculate the area of the given pool.

Observe the figure.

The length of the pool $= 20$ ft

The width of the pool $= 9$ ft

Use equation (1) to find the area of the pool.

The area of the pool $= 20 \times 9 = 180$ ft²

So, the area of the pool is 180 ft².

Step 3. Calculate the area of the given walkway.

The area of the walkway is

the area of the outer rectanglethe area of the inner rectangle

$\begin{array}{l} = (20 + 2 x) (9 + 2 x) - (20 \times 9) \\ = (20 + 2 x) (9 + 2 x) - 180 \end{array}$

Substitute $x = 3$ .

$\begin{array}{l} = (20 + 2 \times 3) (9 + 2 \times 3) - 180 \\ = (20 + 6) (9 + 6) - 180 \\ = (26) (15) - 180 \\ = 390 - 180 \\ = 210 \end{array}$

So, the area of the walkway is 210 ft².

Therefore, the area of the pool is 180 ft² and the area of the walkway is 210 ft².

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Peggy is having a cement walkway installed around the perimeter of her swimming pool with the dimensions shown below. If $x = 3$ find the area, in square feet, of the pool and walkway.

Short Answer

Step by step solution

Step 1. Define the area of the rectangle.

Step 2. Calculate the area of the given pool.

Step 3. Calculate the area of the given walkway.

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Peggy is having a cement walkway installed around the perimeter of her swimming pool with the dimensions shown below. Ifx=3 find the area, in square feet, of the pool and walkway.

Short Answer

Step by step solution

Step 1. Define the area of the rectangle.

Step 2. Calculate the area of the given pool.

Step 3. Calculate the area of the given walkway.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Discrete Mathematics

Probability and Statistics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Peggy is having a cement walkway installed around the perimeter of her swimming pool with the dimensions shown below. If $x = 3$ find the area, in square feet, of the pool and walkway.