Question

BL and CM are medians of a
triangle ABC right angled at A. Prove that
4 (BL? + CM2) = 5 BC.​

Answer 1

Hey mate ✌️✌️✌️

Here is your 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 ........... (2)

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

Hope it helps you..............!!

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