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The image shows a mathematical problem based on the Pythagorean theorem, where a right-angled triangle is given. One leg has a length of 6 units, and the other leg is 8 units. The goal is to find the hypotenuse (denoted as \( x \)).

Here’s a step-by-step breakdown of the solution provided in the image:

1. **Pythagorean theorem**:  
   The formula for the Pythagorean theorem is:  
   \[
   x^2 = a^2 + b^2
   \]
   where \( a \) and \( b \) are the legs of the triangle, and \( x \) is the hypotenuse.

2. **Substitute the values**:  
   Given \( a = 6 \) and \( b = 8 \), we substitute them into the equation:  
   \[
   x^2 = 6^2 + 8^2
   \]
   \[
   x^2 = 36 + 64
   \]
   \[
   x^2 = 100
   \]

3. **Solve for \( x \)**:  
   To find \( x \), take the square root of both sides:  
   \[
   x = \sqrt{100}
   \]
   \[
   x = 10
   \]

Thus, the hypotenuse of the triangle is 10 units.

Would you like more details or explanations? Here are some related questions:

1. What is the Pythagorean theorem used for?
2. Can the Pythagorean theorem be applied to all triangles?
3. How would the formula change if we know the hypotenuse and one leg?
4. What happens if one of the legs is longer than the hypotenuse?
5. How can the Pythagorean theorem be applied to real-world problems?

**Tip:** The Pythagorean theorem only applies to right-angled triangles, where one angle is exactly 90 degrees.

Find the hypotenuse of a right-angled triangle with legs 6 and 8 using the Pythagorean theorem.

Learn how to find the hypotenuse of a right-angled triangle with legs 6 and 8 using the Pythagorean theorem. This step-by-step solution demonstrates the key concepts of geometry and algebra. Suitable for students in Grades 7-9.

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