CBSE Class 10 Maths (Standard) 2019 · Paper 30/4/2 · Question 16(a)

Triangles 3 marks Medium

In Figure 1,

B L

and

C M

are medians of a

△ A B C

right-angled at

A

. Prove that

4 (B L^{2} + C M^{2}) = 5 B C^{2}

Right triangle ABC with medians BL and CM

Answer

Proved:

4 (B L^{2} + C M^{2}) = 5 B C^{2}

, since

B L^{2} + C M^{2} = \frac{5}{4} (A B^{2} + A C^{2})

and

B C^{2} = A B^{2} + A C^{2}

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