The actual length of an object is $50 \, \text{cm}$ when using a scale of $1:10$, and the corresponding drawing length is $5 \, \text{cm}$.

When working with scales, it is essential to recognize that they represent a ratio between the dimensions depicted in a drawing and the actual dimensions of the object. In this example, the scale of $1:10$ indicates that $1$ unit on the drawing corresponds to $10$ units in real life. To determine the actual length of an object, you multiply the drawing length by the scale factor.

In this case, the drawing length is $5 \, \text{cm}$. By applying the scale factor of $10$, you calculate the actual length as follows:

Thus, if an object measures $5 \, \text{cm}$ in the drawing, its real-life length would be $50 \, \text{cm}$.

Understanding scales is vital in various fields, including architecture, engineering, and geography, where precise representations of objects and distances are crucial. By mastering the use and interpretation of scales, you can ensure that your measurements and drawings are both accurate and practical.