Question

BL and CM are medians of a triangle ABC right angled at A. Prove that 4(BL² + CM²) = 5BC².​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given:-

⠀⠀⠀•ABC is a right angled triangle at A. BL and CM are the medians drawn in the triangle ABC.

⠀⠀⠀⠀⠀

Concept:-

⠀⠀⠀•Here the concept of using pythagorus theorum has been clarified.

⠀⠀⠀⠀⠀

To Prove:-

⠀⠀⠀•4(BL²+CM²)=5BC²

⠀⠀⠀⠀⠀

Proof:-

Since,△CAB is a right angled triangle at A

By pythagorus theorum:-

∴⠀⠀⠀BC²=AC²+AB²⠀⠀⠀....(1)

Since,△BAL is a right angled triangle at A

By pythagorus theorum:-

∴ ⠀⠀⠀BL²=AB²+AL²⠀⠀⠀.....(2)

Since,△CAM is a right angled triangle at A

By pythagorus theorum

∴⠀⠀ ⠀CM²=AC²+AM²⠀⠀......(3)

Adding (2) and (3) ,we get

⠀⠀⠀⠀⠀

BL²+CM²=(AB²+AL²)+(AC²+AM²)

➾BL²+CM²=(AB²+AC²)+(AL²+AM²)

➾BL²+CM²=BC²+AL²+AM² [using (1) ]

➾BL²+CM²=BC²+(1/2×AC)²+(1/2×AB)²

[•BL and CM are medians ]

➾ BL²+CM²=BC²+1/4(AC²+AB²)

➾ BL³+CM²=BC²+1/4(BC²) [using (1) ]

➾ BL²+CM²=(4BC²+BC²)/4

➾4(BL²+CM²)=5BC².

Hence, proved