Question

Hexagon A is a regular hexagon. The total length of all the sides of the hexagon is 24 inches. Hexagon A is dilated about its center to create Hexagon B. The length of each side of Hexagon B is 4 4/5 inches. By what factor was Hexagon A dilated to create Hexagon B? A. 5/6 B. 1 1/2 C. 2 D. 4/5

Answer 1

Welcome to Openstudy!

Answer 2

Glad to be here? :D

Answer 3

Okay, so do you know how many sides a hexagon has?

Answer 4

6

Answer 5

Correct, so for the first Hexagon, hexagon A, it has a total of 24 inches. To find the side length of each, we need to divide that by 6.
So what's:
\[\frac{24}{6}\]

Answer 6

4

Answer 7

Right, so each side of hexagon A is 4 inches.
Hexagon B has sides of 4.5 inches.
What's the difference there?

Answer 8

4/5 s? (Hexagon B is 4 4/5, actually) c:

Answer 9

Oh, right sorry I mis-read that. Thanks for the correction.
So what's the difference between
\[4\frac{4}{5}-4=?\]

Answer 10

4/5 c:

Answer 11

Yup, so unless my math skills have suddenly vanished into thin air, that should be the answer.

Answer 12

Actually wait.
\(\dfrac{24}{6}=l_A=4=\dfrac{20}{5}\\
l_b=\dfrac{24}{5}\\
\text{factor of dilation}=\dfrac{l_A}{l_B}=\dfrac{\dfrac{20}{5}}{\dfrac{24}{5}}=\dfrac{5}{6}\)

Answer 13

Thanks Austin, I probably should of asked what dilation was.. ._.