Question 469743
Whenever you have a triangle ABC split into 2 triangles by a bisector through angle B then the following relationship holds:
{{{AK/AB = KC/BC}}}
where AB=18, BC=24, and KC = 28 - AK
{{{AK/18 = (28-AK)/24}}}
Solve for AK:
Multiply by 24 on both sides
{{{(4/3)AK = 28 - AK}}}
Add AK on both sides
**Note: 4/3 + 1 = 4/3 + 3/3 = 7/3 **
{{{(7/3)AK = 28}}}
Multiply by 3/7 on both sides
{{{AK = 12}}}