Question

BL and CM are medians of a triangle ABC right angled at A. Prove that 4(BL² + CM²) = 5BC².

Answer 1

BL and CM are medians at the ΔABC in which

A = ∠90°.

From ΔABC

BC² = AB² + AC² … (1)

(Pythagoras theorem)

4CM² = 4AC² + AB² … (3)

Adding (2) and (3), we have

4(BL² + CM²) = 5(AC² + AB²)

4(BL² + CM²) = 5BC² [From (1)]