If the perimeter of a closed semicircular region is 252 cm, calculate its radius.

We know that the perimeter of the semicircular region can be found by using the formula:

$\mathrm{Perimeter}=\frac{2\mathrm{\pi r}}{2}+2\mathrm{r}$

$\Rightarrow \frac{2\mathrm{\pi r}}{2}+2\mathrm{r}=252$           {$\because$Perimeter is given to be 252 cm}

$\Rightarrow \mathrm{r}(\mathrm{\pi }+2)=252$

$\Rightarrow \mathrm{r}=\frac{252}{{\displaystyle \frac{22}{7}+ 2}}$

$\Rightarrow \mathrm{r}=\frac{252}{{\displaystyle \raisebox{1ex}{$36$}\!\left/ \!\raisebox{-1ex}{$7$}\right.}}$

$\Rightarrow \mathrm{r}=252\times \frac{7}{36}$

$\Rightarrow \mathrm{r}=49 \mathrm{cm}$