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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?

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MrRoyal

Answer:

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

Step-by-step explanation:

Given

Shape: Square

[tex]k = 5[/tex] -- scale factor

[tex]B'C' = 24[/tex]

Required

Side length of ABCD (the hot tub)

From the question, we understand that

[tex]ABCD \to D_5 \to A'B'C'D[/tex]  ABCD dilated by 5 to A'B'C'D

This implies that:

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

So, we have:

[tex]BC * 5 = 24[/tex]

Divide by 5

[tex]BC = 4.8[/tex]

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