To solve for the hypotenuse of the right triangle shown in the image, we can use the Pythagorean theorem, which is:

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

Where:

• $a$ and $b$ are the legs of the triangle (2 cm and 4 cm),
• $c$ is the hypotenuse (the side we need to find).

Substituting the given values:

$2^2 + 4^2 = c^2$

This simplifies to:

$4 + 16 = c^2$

$c^2 = 20$

To find $c$, take the square root of both sides:

$c = \sqrt{20}$

Thus, the length of the hypotenuse is $\sqrt{20} \, \text{cm}$, which simplifies to:

$\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$

The correct answer is D) $\sqrt{20} \, \text{cm}$.

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:

1. How does the Pythagorean theorem apply to right triangles with larger side lengths?
2. What is the significance of perfect square roots versus irrational square roots in geometry?
3. Can you find the area of the triangle using the given sides?
4. How would the hypotenuse change if one leg was doubled in length?
5. What other methods, besides the Pythagorean theorem, can be used to solve right triangles?

Tip: The Pythagorean theorem only applies to right triangles. For non-right triangles, other methods like the Law of Cosines may be used.