Find the radius of the sector adjoining a triangle

Question

We know that the area of the sector should be $\frac{40}{360}\cdot\frac{22}{7}\cdot r^2$

Any ideas on how to begin?

Many Thanks:)

Answer 1

Let $r$ be the radius, then the area of the triangle is $$ A = \frac{1}{2}2 \pi r $$ and the area of the sector is $$ A = \frac{40}{360} \pi r^2 $$ Setting these equal gives you one equation with one unknown $$ \frac{1}{2}2 \pi r = \frac{40}{360} \pi r^2 $$ which you can solve for $r$.