In the right triangle shown, the length of {AC} = 6\] and the length of {BC} = 4\]. What is the length of {AB}



To find the length of side \( AB \) in a right triangle, where \( AC \) and \( BC \) are the legs, we can apply the **Pythagorean Theorem**:

\[
AB^2 = AC^2 + BC^2
\]

Given:
- \( AC = 6 \)
- \( BC = 4 \)

Substitute these values into the equation:

\[
AB^2 = 6^2 + 4^2
\]
\[
AB^2 = 36 + 16
\]
\[
AB^2 = 52
\]

Now, solve for \( AB \):

\[
AB = \sqrt{52}
\]
\[
AB = \sqrt{4 \times 13}
\]
\[
AB = 2\sqrt{13}
\]

So, the length of \( AB \) is \( 2\sqrt{13} \) (approximately 7.21 units).

Would you like further clarification on this or additional details?

Here are 5 related questions for you:
1. What is the Pythagorean Theorem, and why does it apply to right triangles?
2. How can we simplify square roots like \( \sqrt{52} \)?
3. Can the Pythagorean Theorem be applied to non-right triangles?
4. How would the formula change if we were asked to find the length of one of the legs instead of the hypotenuse?
5. What are some real-world applications of the Pythagorean Theorem?

**Tip**: Always simplify square roots as much as possible to present the answer in its simplest form.

In the right triangle shown, the length of AC = 6 and the length of BC = 4. What is the length of AB?

Discover how to calculate the hypotenuse length of a right triangle using the Pythagorean Theorem. With legs AC = 6 and BC = 4, this detailed guide walks you through the step-by-step process of solving for AB = 2√13 (approximately 7.21 units). Perfect for students in Grades 8-10.

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