HELP on this Geometry problem. I'm so stumped!?

Question

In TriangleABC, CM is the median to AB
If the perimeter of triangle...
ABC=18
ACM=15
MCB=15,
then find the measure of CM.
Explain.


This one has me so confused I just need some assistance.

Answer 1

The "trick" is that the median cuts AB into two equal parts, AM and BM. Then we can write
AC+BC+AM+BM=18.
Also that since AC+AM+CM=15, then CM=15-AC-AM. In like manner, CM=15-BC-BM. However, since AM=BM, BC=AC, and the triangle is isoceles. Then 2AC+2AM=18 and AC+AM=9. So CM=15-AC-AM or CM=6.