Question

In ∆ABC, seg AP is a median. If BC = 18, AB² + AC² = 260, find AP.

Answer 1

PC = 1/2 BC [P is the midpoint of side BC] 

= 1/2 × 18 = 9cm 

in ∆ABC, seg AP is the median, 

Now, AB² + AC² = 2A² + 2 PC² [Apollonius theorem] 

∴ 260 = 2AP² + 2 (9)² 

∴ 130 = AP² + 81 [Dividing both sides by 2] 

∴ AP² = 130 – 81 

∴ AP² = 49 

∴ AP = √49 [Taking square root of both sides] 

∴ AP = 7 units