The image shows a right triangle with the following dimensions:

• One leg is $4$,
• The other leg is $2$,
• The hypotenuse is labeled $c$.

To calculate the hypotenuse $c$, we can apply the Pythagorean theorem:

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

Where:

• $a = 4$,
• $b = 2$.

Step-by-Step Solution:

1. Substitute the given values into the formula: $c^2 = 4^2 + 2^2$

2. Square each term: $c^2 = 16 + 4$

3. Add the results: $c^2 = 20$

4. Solve for $c$ by taking the square root: $c = \sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5}$

Thus, the length of the hypotenuse is: $c = 2\sqrt{5} \ (\text{approximately } 4.47).$

Would you like a more detailed breakdown or explanation? Let me know!

Related Questions to Explore:

1. What is the approximate decimal value of $2\sqrt{5}$?
2. How does the Pythagorean theorem apply to other types of triangles?
3. If the hypotenuse is $2\sqrt{5}$, what are the angles of this triangle?
4. How can you use trigonometric ratios to verify this result?
5. What is the area and perimeter of this triangle?

Tip:

In right triangles, always confirm that the largest side is the hypotenuse before applying the Pythagorean theorem.