Question

In the given figure, BL and CM are medians of a triangle ABC right angled at A Prove that 4(BL 2+ CM2)= 5BC2

Answer 1

LHS = 4(BL² + CM²)
= 4{(AL² + AB²) + (AM² + AC²)}
= 4AL² + 4AB² + 4AM² + 4AC²
(2AL²) + 4AB² + (2AM²) + 4AC²
= AC² + 4AB² + AB² + 4AC² (Given AL = LC and AM = MB)
= 5(AC² + AB²)
5BC² = RHS
Hence proved.