Question

Polygons below are similar. Find Z.
Image attached below, so I know I need to make a ratio to see what it is scaled by, but I am not sure where to start with it.

Answer 1

Can someone explain why you get the answer you got too? Thats why I am not showing the answer keys because I need help not just a good guess haha

Answer 2

Did you have a choice of 7.5 there?

Answer 3

@IMStuck I do have that choice. I checked other openstudy questions but people only put the answers, no one really explained it

Answer 4

Ok, I am going to explain it.

Answer 5

If the polygons are similar, that means that their sides are similar in proportion to one another. That means that the side that is 8 units long is similar to the side in the other polygon that is 6 units long. The side that is 10 units long is similar to the side in the other polygon that is z units long. Z is what you need to find. What you need to remember is to keep each proportion for each polygon separate from one another, keeping the similar sides "together". I will show you. You'll get it, just stay with me.

Answer 6

Keeping the polygon ratios separate, I mean like this:
\[\frac{ 8 units }{ 6 units }\]

Answer 7

Those are 2 sides in the same polygon. The other ratio would be set up the same way:
\[\frac{ 10 units }{ "z"units }\]

Answer 8

Then cross multiply?

Answer 9

The side in the first polygon, 8, is in the same position as the side in the other polygon that is 10. So the whole proportion/ratio thing would be set up like this, and then, yes, you will cross multiply to solve for z:
\[\frac{ 8 }{ 6 }=\frac{ 10 }{ z }\]

Answer 10

8 is similar to 10, and 6 is similar to z

Answer 11

Do you understand it now?

Answer 12

I understand how we got there, but I cross multiply and got 13.3333 I think I messed up simplifying somewhere haha 1 second

Answer 13

Yea I wrote down a number wrong I got 7.5 Thank you !

Answer 14

8(z)=6(10)
8z = 60
z = 7.5

Answer 15

And you're welcome!!!!!