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The given triangle is a right triangle, and we can apply the **Pythagorean theorem** to find the value of \( x \). The theorem states:

\[
a^2 + b^2 = c^2
\]

where \( a \) and \( b \) are the legs of the right triangle, and \( c \) is the hypotenuse (the longest side). In this case:

- One leg is \( 6 \, \text{cm} \),
- The hypotenuse is \( 10 \, \text{cm} \),
- We need to find the other leg \( x \).

Now, applying the Pythagorean theorem:

\[
6^2 + x^2 = 10^2
\]

\[
36 + x^2 = 100
\]

\[
x^2 = 100 - 36
\]

\[
x^2 = 64
\]

Taking the square root of both sides:

\[
x = \sqrt{64} = 8 \, \text{cm}
\]

So, the value of \( x \) is **8 cm**.

Would you like any further details or explanations?

Here are some related questions:
1. How can the Pythagorean theorem be applied to solve for a missing hypotenuse?
2. What other methods can you use to find the sides of a right triangle?
3. How does the Pythagorean theorem change if the triangle is not a right triangle?
4. Can you use trigonometric ratios to solve for \( x \) instead of the Pythagorean theorem?
5. What would happen if one of the legs of the triangle was unknown instead of the hypotenuse?

**Tip**: Always check if the triangle is a right triangle before using the Pythagorean theorem!

What is the value for x in the triangle below?

Learn how to solve for x in a right triangle using the Pythagorean Theorem. In this example, a triangle has legs of 6 cm and 10 cm. Suitable for students in Grades 6-8.

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