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Among all sectors of fixed perimeter, ch...

Among all sectors of fixed perimeter, choose the one with maximum area. Then the angle at the center of this sector (i.e.,the angle between the boundibg radii) is

A

`(pi)/(3)`

B

`(3)/(2)`

C

`sqrt(3)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
Given that `2r_rtheta=P" "r=(p)/(2+theta)`
area `=(1)/(2)r^(2)theta=(1)/(2)theta((P)/(2+theta))^(2)=(1)/(2)(P^(2)theta)/((2+theta)^(2))`
`(dA)/(d theta)=0" "theta=2^(C)`
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