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If Delta denotes area of triangle and P ...

If `Delta` denotes area of triangle and P denotes the sum of the 3 sides of triangle then

A

`Delta=(P^(2))/(4)`

B

`Deltale(P^(2))/(12sqrt(3))`

C

`Deltagt(P^(2))/(6sqrt(3))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`P=a+b+cimpliess=(P)/(2)`
`Delta^(2)=s(s" "a)(s-b)(s-c)`
`AMgeGM`
`((s-a)+(s-b)(s-c))/(3)ge((s-a)(s-b)(s-c))^(1//3)`
`(3s-2s)/(3)ge((s-a)(s-b)(s-c))^(1//3)`
`(s)/(3)ge((Delta^(2))^(1//3))/((s^(1//3)))`
`(s^(3))/(27)ge(Delta^(2))/(s)`
`Delta^(2)le(s^(4))/(27)`
`Deltale(s^(2))/(3sqrt(3))implies(P^(2))/(12sqrt(3))`Ans.
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