Question

Please help!!

The options for both of these is right here!

Card A:
16
6
90
9

Card B: Card B *
QR
TU
RS
ST

Answer 1

Given:

Triangle ABC is similar to triangle EFG.

Pentagon ABCDE is similar to pentagon QRSTU.

To find:

The length of segment FG.

The missing value in
`(D)/(EA)=(?)/(UQ)`.

Solution:

In card A,

AC = 15 in.

BC = 9 in.

EG = 10 in.

Triangle ABC is similar to triangle EFG. So, the corresponding sides are proportional.

`(AC)/(BC)=(EG)/(FG)`

Putting the values, we get

`(15)/(9)=(10)/(FG)`

`(5)/(3)=(10)/(FG)`

`5* FG=3* 10`

`5FG=30`

Divide both sides by 5.

`FG=6`

Therefore, the length of segment FG is 6 in.

In card B, pentagon ABCDE is similar to pentagon QRSTU.

The corresponding sides of similar figure are proportional. So,

`(AB)/(QR)=(BC)/(RS)=(CD)/(ST)=(DE)/(TU)=(EA)/(UQ)`

Now,

`(CD)/(ST)=(EA)/(UQ)`

It can be written as

`(CD)/(EA)=(ST)/(UQ)`

Therefore, the missing side is ST.