Question

The perimeter of a rectangle swimming pool Is 84 meters. The width of the pool is 3/4 the length. What are the length and width of the pool?

Answer 1

Given:

Perimeter of rectangular swimming pool = 84 meters

Width of pool = 3/4 of the length

Let's find the length and width of the pool.

Since the swinning pool has the shape of a rectangle and we have the perimeter, to find the length and width, apply the perimeter of a rectangle formula:

$\text{Perimeter = 2(L + W)}$

Where:

L is the length

W is the width.

Given:

W = ¾L

Substitute 84 for perimeter and ¾L for W.

Hence, we have:

$\begin{gathered} P=2(L+W) \\ \\ 84=2(L+\frac{3}{4}L) \end{gathered}$

Let's evealuate the equation and solve for L.

We have:

$\begin{gathered} 84=2(L+0.75L) \\ \\ 84=2(1.75L) \\ \\ 84=3.5L \end{gathered}$

Divide both sides by 3.5:

$\begin{gathered} \frac{84}{3.5}=\frac{3.5L}{3.5} \\ \\ 24=L \\ \\ L=24\text{ meters} \end{gathered}$

To solve for the width W, substitute 24 for L in (W=¾L)

$\begin{gathered} W=\frac{3}{4}\times L \\ \\ W=\frac{3}{4}\times24 \\ \\ W=\frac{3\times24}{4} \\ \\ W=\frac{72}{4} \\ \\ W=18\text{ meters} \end{gathered}$

Therefore, the length of the swimming pool is 24 meters, while the width is 18 meters.

ANSWER:

Length = 24 meters

Width = 18 meters