Question

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

Answer 1

hope it helps! step by step explained

Answer 2

↦Solution : -

REFER TO THE ATTACHMENT ,

BL and CM are medians of the Δ ABC in which ∠A = 90°

From Δ ABC ,

BC² = AB² + AC² (Pythagoras Theorem) [1]

From Δ ABL,

BL² = AL² + AB²

BL² = (AC/2)² + AB² (L is mid-point of AC)

BL² = AC²/4 + AB²

4 BL² = AC² + 4 AB² [2]

From Δ CMA,

CM² = AC² + AM²

CM² = AC² + (AB/2)² (M is mid-point of AB)

CM² = AC² + AB²/4

4 CM² = 4 AC² + AB² [3]

Adding [2] and [3] ,

4 (BL² + CM²) = 5 (AC² + AB²)

i.e. , 4 (BL² + CM²) = 5 BC² [From (1)]