43. Bl and CMare medians of a triangle ABC right angled at A.Prove tha

1.	43. Bl and CMare medians of a triangle ABC right angled at A.Prove that 4(BL2+CMF) 5 BC2
Answer» Given : ABC right angle triangle at A where BL and CM are the medians To prove : 4(BL^2 + CM^2)=5BC^2 Proof :Since BL is the median AL=CL=1/2 AC .............(1) Similarly CM is the median AM = MB = 1/2 AB .......) In triangle ABC BC^2 = AB^2 + AC^2 In triangle BAL BL^2 =AB^2 +AL^2 BL^2 =AB^2 +(AC/2)^2 On further little solving steps 4BL^2 =4AB^2 +AC^2 Then in triangle MAC CM^2 =AM^2 +AC^2 Doing same process here We get 4CM^2 =AB^2 +4AC^2

43. Bl and CMare medians of a triangle ABC right angled at A.Prove that 4(BL2+CMF) 5 BC2

Answer»

Given : ABC right angle triangle at A where BL and CM are the medians

To prove : 4(BL^2 + CM^2)=5BC^2

Proof :Since BL is the median

AL=CL=1/2 AC .............(1)

Similarly CM is the median

AM = MB = 1/2 AB .......)

In triangle ABC

BC^2 = AB^2 + AC^2

In triangle BAL

BL^2 =AB^2 +AL^2

BL^2 =AB^2 +(AC/2)^2

On further little solving steps

4BL^2 =4AB^2 +AC^2

Then in triangle MAC

CM^2 =AM^2 +AC^2

Doing same process here We get

4CM^2 =AB^2 +4AC^2