This is a right-angled triangle problem, where the task is to find the length of the hypotenuse, given the lengths of the two legs (the perpendicular sides).

The formula used for this type of problem is the Pythagorean theorem: $a^2 + b^2 = c^2$ where:

• $a$ and $b$ are the lengths of the legs,
• $c$ is the length of the hypotenuse.

Here, the lengths of the legs are given as $\sqrt{5}$ cm and $\sqrt{20}$ cm.

Substituting into the Pythagorean theorem: $(\sqrt{5})^2 + (\sqrt{20})^2 = c^2$ $5 + 20 = c^2$ $25 = c^2$ Taking the square root of both sides: $c = 5$

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

The correct answer is d) 5.

Let me know if you'd like further explanations or have any other questions! Here are a few related questions you might find interesting:

1. What is the significance of the Pythagorean theorem in geometry?
2. How does the Pythagorean theorem work with non-integer values?
3. What happens if the triangle is not a right triangle?
4. Can the Pythagorean theorem be used in 3-dimensional space?
5. How do you apply the Pythagorean theorem in real-world applications?

Tip: The Pythagorean theorem is essential not only for solving geometry problems but also for determining distances in fields like physics, architecture, and engineering.