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+(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} (84)/(3.5)=(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=(3)/(4)* L \\ \\ W=(3)/(4)*24 \\ \\ W=(3*24)/(4) \\ \\ W=(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