In the figure above, line segment CZ = 6. What is the length of line

Question

https://gmatclub.com/forum/download/file.php?id=35663 In the figure above, line segment CZ = 6. What is the length of line segment AB? (1) Line segment XY = 4 (2) Line segment AZ > Line segment AY Yaz.png

GMATinsight · Answer

Using similar triangle approach

Answer Option A

mohshu · Answer

GMATinsight  can u explain the answer

Leo8 · Answer

FullSizeRender-2.jpg IMHO - Its A

chigpt · Answer

AB/XY =AZ/AZ+YA. 
AB/CZ =AY/AZ+YA
Add both equations
AB=2.4
А is enough to get the answer

Sent from my iPhone using GMAT Club Forum

rausan · Answer

In any such question we can use the following trick
1/xy +1/cz = 1/AB, if it is right angled triangle as here
so, here cz=6
i.e. 1/xy + 1/6 = 1/AB.
ST1- XY=4 SO WE CAN GET AB.- SUFFICIENT ANS IS(A)

sinhap07 · Answer

How are you proving the big triangles similar to the small triangles? One big and one small is possible but how about the other two?

KarishmaB · Answer

Responding to a pm:

We are using the AA property of similarity of triangles. When two angles are the same, the third angle would be the same too since the sum of all three angles of each triangle is 180 degrees. And hence the AAA property of similar triangles is satisfied.

In triangles XYZ and BAZ, angles XYZ and BAZ are 90 degrees each. 
Also, angle BZA and angle XZY are the same angle so they will be equal. 
So these two triangles are similar by AA.

It is the same logic for triangles CZY and BAY.
Angles CZY and BAY are 90 degrees each.
Also angles CYZ and BYA are the same angles so they will be equal. 
So these two triangles are similar by AA.

sinhap07 · Answer

Hi

I get that. But how do we prove the similarity between triangle XYZ and CYZ? Can you pls give the complete solution? How do we even arrive at AB

KarishmaB · Answer

Why do you think they will be similar? Think about it - one of them could be 30-60-90 triangle while another could be 45-45-90.

Posted from my mobile device

bumpbot · Answer

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In the figure above, line segment CZ = 6. What is the length of line

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