Two triangles $PRS$ and $DEF$ are similar whose perimeters are $36\text{cm}$ and $40\text{cm}$, respectively. If the length of $DE$ is $10\text{cm}$, then what is the length (in $\text{cm}$) of $PR$?

For any two similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides.Given:
$$\Delta PRS\sim \Delta DEF$$
$$\text{Perimeter of }\Delta PRS=36\text{cm}$$
$$\text{Perimeter of }\Delta DEF=40\text{cm}$$
$$DE=10\text{cm}$$
The side corresponding to $DE$ in $\Delta PRS$ is $PR$. Therefore:
$$\frac{\text{Perimeter of }\Delta PRS}{\text{Perimeter of }\Delta DEF}=\frac{PR}{DE}$$
Substitute the given values into the formula:
$$\frac{36}{40}=\frac{PR}{10}$$
Solving for $PR$:
$$PR=\frac{36\times 10}{40}$$
$$PR=\frac{36}{4}=9\text{cm}$$