https://file.aiquickdraw.com/mathbot/file/17289082421187fcpxb40.jpg

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.

Using Pythagoras' theorem, calculate the value of x. One leg is 10 cm, the other leg is 24 cm, and the hypotenuse is labeled as x.

Learn how to calculate the hypotenuse using Pythagoras' theorem with a right-angled triangle having legs of 10 cm and 24 cm. The solution involves applying the Pythagorean theorem, perfect for students in Grades 6-8.

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