Task 1270

The task

The circular region of the sign (below, left) has an area of 154 square inches. Vanessa would like to place a tiny ribbon (shaded) around the circle's edge. To be sure she has enough ribbon, she decides to buy 2 inches more of the ribbon than the original circle's circumference. How many inches of ribbon will Vanessa need to buy if she estimates $\pi = \frac{22}{7}$? [asy]import graph; size(125,72.5); picture p; draw(p,unitsquare); filldraw(p,Circle((.5,.5),.3),white); label(p,"Enter",(.5,.5),ZapfChancery("m","n")); add(p); filldraw(Circle((2,.5),.4),gray(.6)); add(shift(1.5*right)*p); draw((1.1,.5)--(1.4,.5),EndArrow(5,25));[/asy]