To determine if the given side lengths form a right triangle, we can apply the Pythagorean Theorem. The theorem states that for a right triangle, the square of the length of the hypotenuse (the longest side) must be equal to the sum of the squares of the other two sides. In mathematical form:

$a^2 + b^2 = c^2$

Here, $a = 6.4$, $b = 12$, and $c = 12.2$ (the longest side is $c$).

Let's check:

$6.4^2 + 12^2 = 12.2^2$

Now, calculate the squares of each side:

$6.4^2 = 40.96, \quad 12^2 = 144, \quad 12.2^2 = 148.84$

Now, sum the squares of $a$ and $b$:

$40.96 + 144 = 184.96$

Since $184.96 \neq 148.84$, the sides do not satisfy the Pythagorean Theorem.

Thus, these lengths do not form a right triangle.

Would you like to explore another similar problem or discuss how to check for right triangles with other methods?

Here are 5 related questions:

1. How do you use the Pythagorean theorem to check for right triangles?
2. Can the lengths 6, 8, and 10 form a right triangle?
3. What if we rearrange the side lengths—how would that affect the result?
4. Can a triangle still be a right triangle if the sides are non-integer values?
5. What happens if one side is slightly longer or shorter in a real-world triangle?

Tip: Always check the longest side first when applying the Pythagorean theorem!