Q8. - Algebra 1

Question

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.

Step-by-Step Solution

Answer

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

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

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

Substitute $x=3$.

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

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.