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

User Saleem Ali
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1 Answer

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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
User Jeff Ward
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