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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.
AB2 + AC2 = 2AM2 + 2BM2 ...[by Apollonius theorem]
290 = 2 (8)2 + 2BM2
290 = 2 (64) + 2BM2
290 = 128 + 2BM2
2BM2 = 290 - 128
2BM2 = 162
BM2 = 81
BM = `sqrt81`
BM = 9 cm
Point M is the midpoint of BC
∴ BC = 2BM = 2 × 9
∴ BC = 18 cm.
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