10.335. The perimeter of a sector is 28 cm, and its area is $49 \mathrm{~cm}^{2}$. Determine the length of the arc of the sector.
## Solution.

The perimeter of the sector $p=2 r+l$, where $r$ is the radius of the sector, $l$ is the length of the arc of the sector. The area of the sector $S=\frac{r l}{2}$.

Then $\left\{\begin{array}{l}2 r+l=28, \\ r l=98,\end{array}\left\{\begin{array}{l}r=\frac{28-l}{2} \\ r l=98\end{array}, l(28-l)=196 ; l^{2}-28 l+196=0 ; l=14\right.\right.$.

Answer: 14 cm.