The perimeter of a triangle with sides measuring $3 \, \text{cm}$, $4 \, \text{cm}$, and $5 \, \text{cm}$ is $12 \, \text{cm}$.

To determine the perimeter of a triangle, you simply sum the lengths of all its sides. In this case, the sides are $3 \, \text{cm}$, $4 \, \text{cm}$, and $5 \, \text{cm}$. Therefore, you calculate the perimeter by adding these three lengths together:

Thus, the perimeter of this triangle is $12 \, \text{cm}$.

This triangle is also classified as a right-angled triangle. This classification is based on the fact that the sides $3 \, \text{cm}$, $4 \, \text{cm}$, and $5 \, \text{cm}$ satisfy the Pythagorean theorem. According to this theorem, in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case:

and

This confirms that it is indeed a right-angled triangle.

Understanding how to calculate the perimeter is an essential skill in geometry. It allows you to determine the total distance around a shape, which can be useful in various practical situations, such as fencing a garden or framing a picture. Always remember to sum all the sides, and you’ll have the perimeter!