Hello! Remember you have to write complete questions in order to get good and exact answers. Anyway, I'll help you either way. A sector is a region of a circle between two radii. Let's assume the sector as:
[tex]s=25\pi cm^2[/tex]
Then, we can find the central angle by the following equation:
[tex]s=\frac{\theta}{360}\times\pi r^{2} \\ \\ r=10cm \\ \\ s=25\pi cm^2 \\ \\ \\ So: \\ \\ \frac{25\pi(360)}{10^2\pi}=\theta \\ \\ \theta = 90^{\circ}[/tex]
But:
[tex]90^{\circ}=\frac{\pi}{2}[/tex]
Then:
[tex]C:Perimeter \ of \ sector \\ \\ \\ C=\theta r \\ \\ C=\frac{\pi}{2}(10) \\ \\ C=5\pi cm \approx \boxed{15.7cm}[/tex]
