ricardo has a square hot tub. he wants to build a square pool next to it that is a dilation of the hot tub…

ricardo has a square hot tub. he wants to build a square pool next to it that is a dilation of the hot tub using a scale factor of 5. if the pool is to be 24 ft on each side, what is the length of one side of the hot tub? 4 ft 4.8 ft 6 ft 7.2 ft

ricardo has a square hot tub. he wants to build a square pool next to it that is a dilation of the hot tub using a scale factor of 5. if the pool is to be 24 ft on each side, what is the length of one side of the hot tub? 4 ft 4.8 ft 6 ft 7.2 ft

Answer

Explanation:

Step1: Recall dilation formula

Let the side - length of the hot - tub be $x$ and the side - length of the pool be $y$, and the scale factor be $k$. The formula for dilation is $y = kx$.

Step2: Substitute known values

We know that $y = 24$ ft and $k = 5$. Substituting into $y = kx$, we get $24=5x$.

Step3: Solve for $x$

To find $x$, we use the equation $x=\frac{y}{k}$. So $x=\frac{24}{5}=4.8$ ft.

Answer:

4.8 ft