To find the length of one side of the hot tub, we need to understand the relationship between the side lengths of the pool and the hot tub, given the scale factor.
1. Identify the scale factor:
The scale factor is given as 5.
2. Understand the scale factor:
Since the pool is built as a dilation of the hot tub, this means that each side of the pool is 5 times as long as each side of the hot tub.
3. Given information:
The side length of the pool is provided as 24 feet.
4. Set up the equation:
Let the side length of the hot tub be [tex]\( x \)[/tex] feet. According to the scale factor relationship:
[tex]\[
\text{Side length of the pool} = \text{Side length of the hot tub} \times \text{Scale factor}
\][/tex]
Substituting the given values:
[tex]\[
24 = x \times 5
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{24}{5}
\][/tex]
6. Calculate the result:
[tex]\[
x = 4.8
\][/tex]
Therefore, the length of one side of Ricardo’s hot tub is [tex]\( 4.8 \)[/tex] feet.
The correct answer is:
[tex]\[
\boxed{4.8 \text{ ft}}
\][/tex]
