In ∆ABC, point M is the midpoint of side BC. If, AB2 + AC2 = 290 cm2, AM = 8 cm, find BC. - Geometry Mathematics 2

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Sum

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

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Solution

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

BM = MC = `1/2` 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.

  Is there an error in this question or solution?
Chapter 2: Pythagoras Theorem - Practice Set 2.2 [Page 43]

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