In the figure shown, segment AB is parallel to segment YZ. If AZ = 42 units, BQ = 8 units, and QY = 28 units, what is the length of segment QZ?

Guest Jan 2, 2021

#1**0 **

Hello Guest!

**Variables: **

If we set line QZ as x, then line AQ would be 42 - x.

QZ = x

AQ = 42 - x

BQ = 8

QY = 28

**Similar:**

The first thing to note is that triangle ABQ is similar to triangle ZYQ.

That also means that the side length ratios are the same.

That means BQ/AQ = QY/QZ

**Equation:**

BQ/AQ = QY/QZ can be written as 8/(42 - x) = x/28.

8/(42 - x) = x/28

1176 - 28x = 8x

1176 = 36x

x = 98/3

**Answer:**

Since x is QZ, our answer is 98/3.

However, I am not the most confident.

I hope this helped. :)))))

=^._.^=

catmg Jan 2, 2021