Here's the explanation:

It is given that BX bisects the angle ABC. Therefore, angle ABX = angle CBX

Also, side AB is similar to side CB and since side BX is common to both triangles ABX and CBX, they are similar.

Using property of similarity, we know that AB/AX = BC/CX

Therefore, by alternando (operation on the above fraction),

AB/BC = AX/CX

We know that AB = 5 and BC = 4

Therefore, AX/CX = 5/4

Performing componendo on both sides,

AX+CX/CX = (5+4)/4 = 9/4

But AX+CX = AC = 7 (given)

Therefore, the above equation becomes 7/CX = 9/4

This can be solved to get the value of CX as 28/9 which is equal to 3.11 cm

Now, we are asked to find the length of AX which is AC-CX

Therefore, AX = 7 - 28/9 = 35/9 = 3.89 cm

Hope this helps.

Cheers!

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MBA Candidate 2015 | Georgetown University

McDonough School of Business