Question

the area of a quadrantis 154 sqcm . find its perimeter

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{r}\mathrm{be}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{circle}. \\ \mathrm{Now},\mathrm{area}\mathrm{of}\mathrm{quadrant}\mathrm{of}\mathrm{circle}=154{\mathrm{cm}}^2 \\ \Rightarrow \frac{1}{4}{\mathrm{\pi r}}^2=154 \\ \Rightarrow \frac{1}{4}\times \frac{22}{7}\times {\mathrm{r}}^2=154 \\ \Rightarrow {\mathrm{r}}^2=49\times 4 \\ \Rightarrow \mathrm{r}=14\mathrm{cm} \\ \mathrm{Now},\mathrm{circumference}=2\mathrm{\pi r}=2\times \frac{22}{7}\times 14=88\mathrm{cm} \end{gathered}$$