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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?

 

 Jan 2, 2021
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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.  :)))))

=^._.^=

 Jan 2, 2021

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