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Question

In ∆ABC, point M is the midpoint of side BC.
If, AB2 + AC2 = 290 cm2, AM = 8 cm, find BC.


Solution

In ∆ABC, point M is the midpoint of side BC.

BM=MC=12BC

AB2+AC2=2AM2+2BM2     by Apollonius theorem290=282+2BM2290=264+2BM2290=128+2BM22BM2=290-1282BM2=162BM2=81BM=9 BC=2×BM           =2×9           =18 cm

Hence, BC = 18 cm.

Mathematics
Mathematics Part - II (Solutions)
Standard X

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