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 = 9 cm

in ∆ABC, seg AP is the median,

Now, AB² + AC² = 2 A^{​​​​​​​2} + 2 PC^{​​​​​​​2} [Apollonius theorem]

∴ 260 = 2 AP² + 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.