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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?

 

 
 Jun 4, 2021
 #1
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Triangle AQB   is similar to Triangle ZQY

 

Therefore

 

AQ / QB  =  QZ  /  QY                    Let   QZ  = x    and  AQ = 42 - x ......so....

 

(42 - x)  /  8  =     x  /  28               cross-multiply

 

28 (42 - x)  =  8x

 

28*42  -  28x  =  8x

 

28*42  =   8x  + 28x

 

1176  =  36x

 

1176/36   =  x  =  98/3   =  QZ 

 

 

cool cool cool

 
 Jun 4, 2021

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