https://file.aiquickdraw.com/mathbot/file/172675436259618r72gsn.jpg

The image shows a right-angled triangle with the two legs labeled \(\sqrt{30} \, \text{m}\) and \(\sqrt{2} \, \text{m}\), and the hypotenuse labeled as \(x\). To solve for \(x\), we can apply the Pythagorean theorem, which states:

\[
x^2 = (\text{leg}_1)^2 + (\text{leg}_2)^2
\]

Substituting the given values:

\[
x^2 = (\sqrt{30})^2 + (\sqrt{2})^2
\]

Simplifying:

\[
x^2 = 30 + 2 = 32
\]

So:

\[
x = \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2} \, \text{m}
\]

Therefore, \(x = 4\sqrt{2} \, \text{m}\).

Do you have any questions or would you like a further breakdown of the steps?

Here are 5 related questions:
1. How do you calculate the square of a square root?
2. What are the properties of a right triangle?
3. How do you simplify \(\sqrt{32}\)?
4. What is the Pythagorean theorem and when is it used?
5. Can the value of \(x\) be expressed as a decimal approximation?

**Tip:** Always ensure that the triangle is a right triangle when applying the Pythagorean theorem!

Find the hypotenuse of a right-angled triangle where the legs are \(\sqrt{30} \, \text{m}\) and \(\sqrt{2} \, \text{m}\).

Learn how to find the hypotenuse of a right-angled triangle where the legs are \(\sqrt{30} \, \text{m}\) and \(\sqrt{2} \, \text{m}\) using the Pythagorean theorem. This step-by-step guide simplifies \(\sqrt{32}\) to provide the exact length of the hypotenuse. Suitable for Grades 9-10 students.

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