Question

In ∆ABC AP is median BC=18cm AB²+AC=260cm².find AP​

Answer 1

Answer:

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