The image shows a right-angled triangle with one leg measuring 10 cm, another leg measuring 24 cm, and the hypotenuse labeled as $x$. To find the value of $x$, we can use the Pythagorean Theorem, which is:

$x^2 = a^2 + b^2$

where $a$ and $b$ are the lengths of the two legs of the right triangle, and $x$ is the hypotenuse.

In this case:

• $a = 10 \, \text{cm}$
• $b = 24 \, \text{cm}$

Now, substituting the values:

$x^2 = 10^2 + 24^2$ $x^2 = 100 + 576$ $x^2 = 676$

Taking the square root of both sides:

$x = \sqrt{676} = 26$

Therefore, the value of $x$ is 26 cm.

Would you like any further explanation or have any questions?

Here are five related questions to deepen your understanding:

1. How would the result change if one of the legs was longer?
2. Can you use the Pythagorean theorem for any triangle?
3. How do you know when a triangle is a right triangle?
4. How would you solve this problem if the hypotenuse was given instead of one of the legs?
5. What are some real-life applications of the Pythagorean theorem?

Tip: The Pythagorean theorem only applies to right-angled triangles. Make sure to verify the type of triangle before applying it.