SOLUTION: Hi, I'm having trouble with this particicular setup of the equation. I'm really not quite sure how to solve it. Any help would be greatly appreciated. Thanks! Stefani In trian

Algebra ->  Triangles -> SOLUTION: Hi, I'm having trouble with this particicular setup of the equation. I'm really not quite sure how to solve it. Any help would be greatly appreciated. Thanks! Stefani In trian      Log On


   

Question 469743: Hi,
I'm having trouble with this particicular setup of the equation. I'm really not quite sure how to solve it. Any help would be greatly appreciated. Thanks!
Stefani
In triangle ABC, the bisector of anlge B meets AC at K. AB= 18, BC= 24,and AC= 28. Find AK.
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Whenever you have a triangle ABC split into 2 triangles by a bisector through angle B then the following relationship holds:
AK%2FAB+=+KC%2FBC
where AB=18, BC=24, and KC = 28 - AK
AK%2F18+=+%2828-AK%29%2F24
Solve for AK:
Multiply by 24 on both sides
%284%2F3%29AK+=+28+-+AK
Add AK on both sides
**Note: 4/3 + 1 = 4/3 + 3/3 = 7/3 **
%287%2F3%29AK+=+28
Multiply by 3/7 on both sides
AK+=+12