Question

Hexagon A is a regular hexagon. The total length of all the sides of the hexagon is 30 inches. Hexagon A is dilated about its center to create Hexagon B. The length of each side of Hexagon B is 3 and 3 over 4 inches.

By what factor was Hexagon A dilated to create Hexagon B?

1 and 1 over 4

1 and 1 over 3

5


3 over 4

Answer 1

Hexagons A has 6 sides, and the total length of all the sides is 30 inches. Can you tell me how long each side will be? (Remember, it's a regular hexagon so they'll all be the same size).

Answer 2

umm i still dont really get it :/

Answer 3

Ok, well if the total length of all the sides is 30 inches and there are 6 sides which each have the same length, then to work out the length of one side all we have to do is divide 30 inches by 6.
So each side of hexagon A has length \(30\div 6=5 \) inches. Agree so far?

Answer 4

yea

Answer 5

Good, then to find the dilation factor all we do is work out:
\[\frac{\text{New length of each side}}{\text{Old length of each side}}\]
Do you think you can do that?

Answer 6

how do you find new length of each side?

Answer 7

It's given to you in the question, read again :)

Answer 8

It tells you what the length of each side is after the dilation.

Answer 9

i dont know how to cause its fraction and am not good with fractions

Answer 10

Ok, do you want to just tell me in words what we will do and I'll write the fraction out?

Answer 11

ok so what i think am supposed to do is write 3&3/4 divide by whatever the old length is

Answer 12

Excellent :) Do you know how to convert 3 and 3/4 to a top heavy fraction?

Answer 13

This will make the next step a bit easier.

Answer 14

9/4 i think

Answer 15

Not quite, if we want 3 and 3/4 as a fraction over 4 we just add \(3\times 4\) to the top of the fraction, so we'll have \(\frac{15}{4}\). Do you see why this is?

Answer 16

oh yea i see

Answer 17

Great :) So as you said, we now divide that by 5:
\[\frac{(\frac{15}{4})}{5}\]
Do you think you can tell me what that is?

Answer 18

If not I'll give you a hint.

Answer 19

i got 3/4

Answer 20

Very good :)

Answer 21

yayyy, wow after going through it with me i realize it wasn't so hard.. thank you :)

Answer 22

Good work, no problem at all :)