plzzzzzzzzzz give the ansr with explanation
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Here's the answer!!!!
Step-by-step explanation:
Here you go....
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To Prove
4(BL² + CM²) = 5BC²
Here, since BL and CM are medians, we get
AL = AC/2 and AM = AB/2
Now, apply Pythagoras theorem in ΔABL,
AB² + AL² = BL²
⇒ AB² + (AC/2)² = BL²
⇒ AB² + AC²/4 = BL².........................(1)
Again, apply Pythagoras theorem in ΔAMC
AC² + AM² = CM²
⇒ Ac² + (AB/2)² = CM²
⇒ AC² + AB²/4 = CM².....................................(2)
In ΔABC,
AB² + AC² = BC² .................(3)
Now, add (1) and (2)
BL² + CM² = AB² + AC² + AB²/4 + AC²/4
Multiply by 4 on both sides,
⇒ 4(BL² + CM²) = 4AB² + 4AC² + AB² + AC²
⇒ 4(BL² + CM²) = 5AB² + 5AC²
⇒ 4(BL² + CM²) = 5(AB² + AC²)
⇒ 4(BL² + CM²) = 5BC² (From (3))
Hence Proved.
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