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To find the length of the third side in the right triangle, we can use the **Pythagorean Theorem**:

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

Where:
- \(a\) and \(b\) are the lengths of the legs of the triangle,
- \(c\) is the length of the hypotenuse (the side opposite the right angle).

In this case, we are given the two legs: \(16\) and \(12\). We need to find \(c\), the length of the hypotenuse.

Substitute the values:

\[
16^2 + 12^2 = c^2
\]

\[
256 + 144 = c^2
\]

\[
400 = c^2
\]

Now, take the square root of both sides:

\[
c = \sqrt{400} = 20
\]

So, the length of the third side (the hypotenuse) is **20**.

Would you like more details or have any questions?

Here are some related questions to explore further:
1. What is the Pythagorean theorem used for in real-life applications?
2. Can you solve for a leg if the hypotenuse and one leg are given?
3. How do you handle non-right triangles for side lengths?
4. What if one of the sides includes a decimal, how do you adjust the calculation?
5. What are the properties of a 3-4-5 right triangle?

**Tip**: Always check if your triangle fits common Pythagorean triples to save time when solving for the third side.

Find the length of the third side of a right triangle with legs of lengths 16 and 12.

Learn how to solve for the hypotenuse of a right triangle with legs of lengths 16 and 12 using the Pythagorean Theorem. This detailed solution involves key geometry concepts and the famous a^2 + b^2 = c^2 formula. Suitable for middle school students (Grades 6-8).

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