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

Step-by-step solution

Perimeter =2 r + r = k (const.) Area = 2 r ²= 1 2 ( k -2 r ) r A = 1 2 ( kr -2 r ² ) d A dr = 1 2 ( k -4 r )=0 r = k 4 d ² ~A dr ² < 0 So, 2 r +2 = k array l k 2 + k 4 = k =2 array