To find the length of the third side of the right triangle in the image, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle:

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

where $c$ is the hypotenuse (the side opposite the right angle), and $a$ and $b$ are the other two sides.

From the image:

• One leg $a = 1$ unit
• The other leg $b = 5$ units

We are looking for the length of the hypotenuse $c$.

Plugging the values into the Pythagorean Theorem:

$c^2 = 1^2 + 5^2$ $c^2 = 1 + 25$ $c^2 = 26$ $c = \sqrt{26}$

Now, let's calculate $\sqrt{26}$ and round to the nearest tenth:

$c \approx 5.1 \text{ units}$

So, the length of the third side is approximately 5.1 units.

Would you like more details or have any questions about this process?

Here are 5 related questions:

1. How would the Pythagorean Theorem be applied if you were given the hypotenuse and one leg?
2. What is the importance of the Pythagorean Theorem in different areas of mathematics?
3. How can you determine if a triangle is a right triangle using the side lengths alone?
4. What are some real-world applications of the Pythagorean Theorem?
5. Can the Pythagorean Theorem be applied to non-right triangles?

Tip: When working with right triangles, always identify the right angle first to correctly assign the sides as legs or the hypotenuse.