This problem involves finding the hypotenuse of a right-angled triangle using the Pythagorean theorem, which states:

$a^2 + b^2 = c^2$

Where:

• $a$ and $b$ are the lengths of the legs of the triangle.
• $c$ is the length of the hypotenuse (the side opposite the right angle).

From the image:

• One leg is 3 cm.
• The other leg is 4 cm.
• The hypotenuse (denoted as $x$) is the unknown side.

We substitute the known values into the Pythagorean theorem:

$3^2 + 4^2 = x^2$

$9 + 16 = x^2$

$x^2 = 25$

$x = \sqrt{25} = 5$

Therefore, the missing length of the hypotenuse is 5 cm.

Would you like further details or explanations?

Here are some related questions for practice:

1. What would happen if the lengths of the legs were doubled?
2. How do you solve for the missing leg if the hypotenuse and one leg are known?
3. What are other applications of the Pythagorean theorem?
4. Can you use the Pythagorean theorem in 3D space? How?
5. What is the importance of the Pythagorean theorem in real-life scenarios?

Tip: Always check if the triangle is right-angled before applying the Pythagorean theorem!