Question

solve it please fast n no spam

Answer 1

Heya !!

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Given :- BL and CM are medians of ∆ABC in which angle A = 90°

To prove :- 4 (BL²+CM²) = 5 BC²

Proof :- From ∆ABC,
BC²=AB²+AC² (Pythagoras Theorem) _(1)

From ∆ABL,
BL²=AL²+AB²
=> BL²= (AC/2)² + AB² (L is the mid-point of AC)
=> BL²=(AC²/4) + AB²
=> 4BL² = AC²+4AB² _(2)

From ∆CMA,
CM²=AC²+AM²
=> CM² = AC² + (AB/2)² (M is the mid-point of AB)
=> CM² = AC² + (AB²/4)
=> 4CM² = 4AC² + AB² _(3)

Adding (2) and (3),
4 (BL² + CM²) = 5 (AC² + AB²)
i.e., 4 (BL² + CM²) = 5 BC² [ From (1) ]

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Hopr my ans.'s satisfactory. ☺