To determine the length of one side of Ricardo's hot tub, we need to use the concept of dilation with a given scale factor. Here’s a step-by-step explanation of how to solve the problem:
1. Understand the Problem:
- We know the side length of the square pool, which is 24 feet.
- The pool is a dilation of the hot tub.
- The scale factor for the dilation is 5.
2. Set Up the Equation:
- Let's denote the length of one side of the hot tub as [tex]\( x \)[/tex].
- Since the pool is a dilation of the hot tub by a scale factor of 5, the relationship between the side lengths can be stated as:
[tex]\[
\text{Side length of pool} = \text{Scale factor} \times \text{Side length of hot tub}
\][/tex]
- Substituting the known values, we get:
[tex]\[
24 = 5 \times x
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
- To find [tex]\( x \)[/tex], we need to isolate it on one side of the equation. We do this by dividing both sides of the equation by 5:
[tex]\[
x = \frac{24}{5}
\][/tex]
4. Simplify the Fraction:
- Simplifying the right side of the equation gives us:
[tex]\[
x = 4.8
\][/tex]
5. Conclusion:
- The length of one side of Ricardo’s hot tub is 4.8 feet.
Therefore, the correct answer to the question is:
4.8 ft.
