Question

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

Answer 1

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

∴ seg AM is the median. 

∴ AB² + AC² = 2 AM² + 2 MC² [Apollonius theorem] 

∴ 290 = 2 (8) + 2 MC² 

∴ 145 = 64 + MC² [Dividing both sides by 2] 

∴ MC² = 145 – 64 

∴ MC² = 81 

∴ MC = \(\sqrt {81}\) [Taking square root of both sides] 

MC = 9 cm 

Now, BC = 2 MC [M is the midpoint of BC]

= 2 × 9 

∴ BC = 18 cm