Question

Given: ΔABC, CM ⊥ AB AC = 10, CM = 4 AM:BM = 2:5 Find: AB, CB

Answer 1

Remark that the triangle AMC is right.
Therefore

`10^2=4^2+AM^2\text{ Pythagorian formula}`
Solving the above equation for AM we get

`AM=9.2`
Since

`(AM)/(BM)=(2)/(5)\text{ then }BM=(5)/(2)AM=(5)/(2)*9.2=23`
Conclusion:

`AB=AM+BM=9.2+23=32`
We use the Pythagorian formula on the right angles triangle MBC like this:

`BC^2=4^2+23^2\text{ then }BC=23.3`