To find the hypotenuse $c$ of a right triangle when the lengths of the legs $a$ and $b$ are known, we can use the Pythagorean theorem:

$c = \sqrt{a^2 + b^2}$

In this case:

• $a = 10$
• $b = 24$

Substitute these values into the formula:

$c = \sqrt{10^2 + 24^2}$

Calculate $10^2$ and $24^2$:

$10^2 = 100 \quad \text{and} \quad 24^2 = 576$

Add them together:

$100 + 576 = 676$

Now, take the square root of 676:

$c = \sqrt{676} = 26$

Answer:

The length of the hypotenuse $c$ is 26.

Would you like further details or have any questions?

Here are some related questions you might find useful:

1. How does the Pythagorean theorem apply to different triangle types?
2. How would you find a leg length if you only know $c$ and the other leg?
3. What are some practical applications of the Pythagorean theorem?
4. How do you verify if a triangle is a right triangle using side lengths?
5. How would rounding affect the hypotenuse if the leg lengths were decimal values?

Tip: Always check if you need an exact or rounded answer when working with square roots!