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

Answer:

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

Step-by-step 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

$BC = 4.8$