Question

Which set can represent the side lengths of a right triangle?

Answer 1

The set that represents a right triangle has to satisfy Pythagorean's Theorem where the greatest side is the hypothenuse. Let's evaluate each of them until we get the right set.

`\begin{gathered} 7^2=6^2+(\sqrt[]{21})^2 \\ 49=36+21 \\ 49=57 \end{gathered}`
`\begin{gathered} (5\sqrt[]{3})^2=7^2+5^2 \\ 25\cdot3=49+25 \\ 75=74 \end{gathered}`

`\begin{gathered} (2\sqrt[]{5})^2=4^2+2^2 \\ 4\cdot5=16+4 \\ 20=20 \end{gathered}`

As you can observe, set B satisfies the theorem.

Hence, B is the answer.