Question

Determine whether the set of side lengths form a right triangle

Answer 1

The side lengths will form a right triangle if they satisfy the pythagorean theorem. So:

`\begin{gathered} c^2=a^2+b^2 \\ where \\ c>a \\ c>b \\ so\colon \\ a=9 \\ b=12 \\ c=15 \\ thus \\ 15^2=9^2+12^2 \\ 225=81+144 \\ 225=225 \\ this_{\text{ }}is_{\text{ }}true \end{gathered}`

Therefore, they form a right triangle