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If in any triangle, the area DeltaABC le...

If in any triangle, the area `DeltaABC le(b^(2)+c^(2))/(lambda)`, then the largest possible numerical value of `lambda` is

A

1

B

2

C

3

D

4

Text Solution

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The correct Answer is:
D
`Delta le(b^(2)+c^(2))/(lambda)`
`rArr (1)/(2)bc sin A le(b^(2)+c^(2))/(lambda)`
`rArr bc((1)/(2)lambda sin A-2)le (b-c)^(2)`
Since sin `A le 1`, the above inequality will always be satisfied if `lambda = 4`
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