Select 3 side lengths that can form a right triangle. \begin{tabular}{|l|l|l|}\hline 12 centimeters & 14 centimeters & 16 centimeters \ \hline 30 centimeters & 32 centimeters & 34 centimeters \ \hline\end{tabular}

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To determine which set of side lengths can form a right triangle, we can use the Pythagorean theorem. According to this theorem, for a triangle with sides $$a$$, $$b$$, and $$c$$ (where $$c$$ is the longest side), the following condition must hold:

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

Let's evaluate both sets of side lengths provided:

1. **First set: 12 cm, 14 cm, 16 cm**
   - Here, $$c = 16$$, $$a = 12$$, and $$b = 14$$.
   - We will check if $$12^2 + 14^2 = 16^2$$.

$$
   12^2 = 144
   $$
   $$
   14^2 = 196
   $$
   $$
   16^2 = 256
   $$

Now, we calculate:

$$
   144 + 196 = 340 \quad \text{(not equal to 256)}
   $$

Therefore, the first set does not form a right triangle.

2. **Second set: 30 cm, 32 cm, 34 cm**
   - Here, $$c = 34$$, $$a = 30$$, and $$b = 32$$.
   - We will check if $$30^2 + 32^2 = 34^2$$.

$$
   30^2 = 900
   $$
   $$
   32^2 = 1024
   $$
   $$
   34^2 = 1156
   $$

Now, we calculate:

$$
   900 + 1024 = 1924 \quad \text{(not equal to 1156)}
   $$

Therefore, the second set also does not form a right triangle.

Since neither set of side lengths satisfies the Pythagorean theorem, neither can form a right triangle.
Neither set of side lengths can form a right triangle.

Select 3 side lengths that can form a right triangle. \begin{tabular}{|l|l|l|}\hline 12 centimeters & 14 centimeters & 16 centimeters \\ \hline 30 centimeters & 32 centimeters & 34 centimeters \\ \hline\end{tabular}

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