Question

The perimeter of a sector is p. The area of the sector is maximum when its radius is​

Answer 1

Answer:

3 is the area of sector is maximum

Answer 2

Answer: r = p/4

Step-by-step explanation:

p = 2r + rθ  ⇒ θ = (p - 2r)/r

A = $r^2$θ/2 = $r^2$(p - 2r)/2r =  $\frac{pr}{2} -r^2$

so maximize  $\frac{pr}{2} -r^2$

$\frac{pr}{2} -r^2 =\frac{ p^2}{16} -\frac{ p^2}{16} + \frac{pr}{2} -r^2$

$\frac{pr}{2} -r^2 =\frac{ p^2}{16} - (\frac{p}{4}-r )^2$

so, it is maximum when p/4 - r =0

⇒ r = p/4