Answer:
C. 9, 40, 41
Explanation:
To determine if the set of dimensions would make a right triangle, we use the Pythagorean Theorem.
Note that the longest length is always the hypotenuse.
Option A
[tex]\begin{gathered} 10^2=8^2+7^2 \\ 100=64+49 \\ 100\ne113 \end{gathered}[/tex]Option B
[tex]\begin{gathered} 31^2=20^2+21^2 \\ 961=400+441 \\ 961\ne841 \end{gathered}[/tex]Option C
[tex]\begin{gathered} 41^2=9^2+40^2 \\ 1681=81+1600 \\ 1681=1681 \end{gathered}[/tex]Option D
[tex]\begin{gathered} 13^2=11^2+5^2 \\ 169=121+25 \\ 169\ne146 \end{gathered}[/tex]The set of dimensions that would make a right triangle is 9, 40 and 41.
