Question

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

Explanation:

Step1: Recall the dilation formula

The formula for dilation is \( \text{Image length}=\text{Scale factor}\times\text{Pre - image length}\). Let the side length of the hot - tub be \(x\). The scale factor \(k = 5\) and the side length of the pool (image) \(y=24\) ft. So, \(y = kx\).

Step2: Solve for \(x\)

Substitute \(y = 24\) and \(k = 5\) into the formula \(y=kx\). We get \(24 = 5x\). Then, \(x=\frac{24}{5}\).

$$x = 4.8$$

Answer:

4.8 ft