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. Point Q is the center of dilation. Square A B C D is dilated to created square A prime B prime C prime D prime. The length of B prime C prime is 24 feet. If the pool is to be 24 ft on each side, what is the length of one side of the hot tub?

Answer 1

The length of one side of the hot tub is 4.8ft

Explanation:

Given

Shape: Square

`k = 5` -- scale factor

`B'C' = 24`

Required

Side length of ABCD (the hot tub)

From the question, we understand that

`ABCD \to D_5 \to A'B'C'D` ABCD dilated by 5 to A'B'C'D

This implies that:

`BC * 5 = B'C'` i.e. the sides of ABCD is multiplied by 5 to get A'B'C'D

So, we have:

`BC * 5 = 24`

Divide by 5

`BC = 4.8`