Question

BL and CM are medians of triangle ABC , right angled at A , Prove that 4(BL square +CM square)=5 BC square.

Answer 1

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

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Answer 2

Answer:

Step-by-step explanation:

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