Question

BL&CM are medians of triangle ABC right angled at A. prove that 4(BL^2 +CM^2) =5BC^2.

Answer 1

hey friends ☺

Given - A ∆ABC in which BL and CM are median of triangle and <A =90°

to proove-- 4(BL²+CM²) = 5 BC²

proof --In ∆ABC ,<A=90°

BC ² =AB ² +AC ²---1) [ by Pythagoras theorem ]

in ∆BAL ,<A =90°

=>BL ² = AL ² + AB ²

=>BL² = (1/2AC)² + AB² [ by Pythagoras theorem ]

=>4BL² = AC² +4AB²-----------2)

in ∆CAM ,<A =90°

•°• CM² =AM² +AC²

=>CM² = (1/2AB)² +AC²

=>CM² = (1/2AB)² + AC²

=>4CM² = AB² +4AC² --------------3)

now ,on adding 2) and 3 ) we get .

4(BL² + CM² )=5(AB²+AC²)

4(BL²+CL² )=5BC² ...from 1)
prooved. here ..

hope it helps you .

@Rajukumar111a