BL and CM are medians of a triangle ABC right angled at A. Prove that

1.	BL and CM are medians of a triangle ABC right angled at A. Prove that 4(Bl + CM2)=5BCIf a1,21 then two linesa2 b2
Answer» let,AM=MB=x and AL=LC=y. now,LHS=4(BL^2+CM^2) =4[{(2x)^2+(y)^2}+{(2y)^2+(x)^2}] (by pythagoras theorem) =4[4x^2+y^2+4y^2+x^2] =4[5x^2+5y^2] =20x^2+20y^2 …… (1) and now,RHS=5BC^2 =5[(2x)^2+(2y)^2] (since by pythagoras theorem h^2=b^2+p^2,p=perpndicular, b=base and h=hypotenuse) =5[4x^2+4y^2] =20x^2+20y^2 ……(2) LHS=RHS hence,proved Hit like if you find it useful!

BL and CM are medians of a triangle ABC right angled at A. Prove that 4(Bl + CM2)=5BCIf a1,21 then two linesa2 b2

Answer»

let,AM=MB=x and AL=LC=y.

now,LHS=4(BL^2+CM^2)

=4[{(2x)^2+(y)^2}+{(2y)^2+(x)^2}] (by pythagoras theorem)

=4[4x^2+y^2+4y^2+x^2]

=4[5x^2+5y^2]

=20x^2+20y^2 …… (1)

and now,RHS=5BC^2

=5[(2x)^2+(2y)^2] (since by pythagoras theorem h^2=b^2+p^2,p=perpndicular, b=base and h=hypotenuse)

=5[4x^2+4y^2]

=20x^2+20y^2 ……(2)

LHS=RHS

hence,proved

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