Given that the perimeter of the triangle is 100 cm, and the lengths of two sides are 30 cm and 40 cm, we can find the length of the third side using the formula for the perimeter of a triangle:

$\text{Perimeter} = a + b + c$

Where $a$, $b$, and $c$ are the lengths of the three sides of the triangle.

In this case:

• $a = 30$ cm
• $b = 40$ cm
• The perimeter = 100 cm

We need to find the length of the third side $c$.

$100 = 30 + 40 + c$

Simplifying the equation:

$100 = 70 + c$

Now, solving for $c$:

$c = 100 - 70 = 30 \, \text{cm}$

Thus, the length of the third side is 30 cm.

Would you like more details or have any questions?

Here are some related questions:

1. What happens if the perimeter of the triangle changes?
2. Can a triangle have sides of any length?
3. What if one of the given sides was larger than the perimeter minus the other sides?
4. How does the triangle inequality theorem apply here?
5. Can you calculate the area of this triangle using the given sides?

Tip: The sum of the lengths of any two sides of a triangle must always be greater than the third side (Triangle Inequality Theorem).