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AP EAMCET2006MathematicsProperties of Triangles

The perimeter of a sector is a constant. If its area is to be maximum, the sectorial angle is :

Options

  1. A^c 6
  2. B^c 4
  3. C4^c
  4. D2^c

Correct answer

D. 2^c

Step-by-step solution

Let length of sector is land radius of sector is r . l= 2 r 360^ Perimeter of sector P= 2 r 360^ +2 r P= ( 2 360^ +2 ) r r= P ( 2 360^ +2 ) A= r^2 360^ A= 360^ [ P^2 ( 2 360^ +2 )^2 ] = P^2 360^ [ ( 2 360^ +2 )^2 ] d A d = P^2 360^ [ ( 2 360^ +2 )^2- 2 ( 2 360^ +2 ) 360^ ( 2 360^ +2 )^4 ] Put d A d =0 , for maxima or minima ( 2 360^ +2 )- 4 360^ =0 180^ =2 = 2 180^ =2 rad Thus Area of sector will be maximum, if sectorial angle is of 2 rad .

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