ABC is a right angled triangle at B , BM is a median on side AC(AM=MC). AB=3,BC=4 and MC=5 ,then find the value of BM
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Given, △ABC, M is mid point of AB and N is mid point of BC.
In △ABN,
AN
2
=AB
2
+BN
2
(Pythagoras Theorem)
AN
2
=AB
2
+(
2
BC
)
2
....(1)
In △BMC,
MC
2
=BM
2
+BC
2
(Pythagoras Theorem)
MC
2
=BC
2
+(
2
AB
)
2
....(2)
Add (1) and (2),
AN
2
+MC
2
=AB
2
+(
2
BC
)
2
+BC
2
+(
2
AB
)
2
AN
2
+MC
2
=
4
5
AB
2
+
4
5
BC
2
4(AN
2
+MC
2
)=5(AB
2
+BC
2
)
4(AN
2
+MC
2
)=5AC
2
(Pythagoras Theorem in △ABC)
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