Question

A town plans to build a new swimming pool. An Olympic pool is rectangular with a length of 50 meters and a width of 25 meters. The new pool will be similar in shape to an Olympic pool but will have a length of 40 meters. Find the perimeters of an Olympic pool and the new pool.

Answer 1

To find the perimeters of both the Olympic pool and the new pool, we can use the formula for the perimeter \( P \) of a rectangle, which is given by:

\[
P = 2 \times (\text{length} + \text{width})
\]

### Step 1: Calculate the perimeter of the Olympic pool

- Length = 50 meters
- Width = 25 meters

Substituting these values into the perimeter formula:

\[
P_{\text{Olympic}} = 2 \times (50 + 25) = 2 \times 75 = 150 \text{ meters}
\]

### Step 2: Determine the dimensions of the new pool

The new pool is similar in shape to the Olympic pool, which means it maintains the same ratio of length to width. For the Olympic pool:

\[
\text{Length} : \text{Width} = 50 : 25 = 2 : 1
\]

With the new pool having a length of 40 meters, we can use the ratio to find the width. Since the ratio of length to width is 2:1, we can set up the proportion:

\[
\frac{\text{Length}}{\text{Width}} = 2 \implies \text{Width} = \frac{\text{Length}}{2} = \frac{40}{2} = 20 \text{ meters}
\]

### Step 3: Calculate the perimeter of the new pool

Now that we have the new dimensions:

- Length = 40 meters
- Width = 20 meters

Substituting these values into the perimeter formula:

\[
P_{\text{New}} = 2 \times (40 + 20) = 2 \times 60 = 120 \text{ meters}
\]

### Summary of Results

- Perimeter of the Olympic pool: **150 meters**
- Perimeter of the new pool: **120 meters**