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.