To know if he can make a right triangle with those lengths, we have to use Pythagorean's Theorem.
[tex]h^2=l^2_1+l^2_2[/tex]This theorem associates the square of the hypothenuse (longer side) with the length of both legs. Let's replace the given values to see if they satisfy the theorem.
[tex]\begin{gathered} 15^2=6^2+9^2 \\ 225=36+81 \\ 225=117 \end{gathered}[/tex]As you can see, the given lengths do not satisfy the theorem.
