Question 5
BL and CM are medians of a triangle ABC right angled at A. Prove that 4 (BL2 + CM2) = 5 BC2.
Given:
Δ ABC right angled at A ,i.e., ∠ 𝐴=90°
Where BL and CM are the medians
To Prove: 4(BL2 + CM2) = 5 BC2
Proof :-
Since BL is the median,
AL = CL = 1/2 AC
Similarly, CM is the median
AM = MB = 1/2 AB
We know that, by Pythagoras theorem
(Hypotenuse)2 = (Height)2 + (Base)2
Now,
(BC)2 = (AB)2 + (AC)2 …(1)
4BL2 = 4(AB)2 + AC2 …(2)
4 CM2 = AB2 + 4 AC2 …(3)
Adding (2) and (3)
4 BL2 + 4CM2 = 4AB2 + AC2 + AB2 + 4AC2
4(BL2 + CM2) = 5AB2 + 5AC2
4(BL2 + CM2) = 5 (AB2 + AC2)
4(BL2 + CM2) = 5 BC2
Hence proved

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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