Question 854810
r is the unknown radius.

The circumference (of the circle) would be 2*pi*r, and the arc length portion of the sector is {{{((pi/4)/(2*pi))*(2*pi*r)}}}; which we should simplify NOW:


{{{ArcPortion=(pi*r)/4}}}


The perimeter of the sector is the sum of two of r and the ArcPortion:
Given that the perimeter is 12,
{{{highlight(2r+(pi*r)/4=12)}}}
This is now a fairly simple equation easily solvable for r.