Solution:
To know which measure would be correct for the lengths of the sides of a right triangle, the Pythagorean triple is used.
[tex]a^2+b^2=c^2[/tex][tex]\begin{gathered} 2^2+3^2=4+9=13 \\ 4^2=16 \\ Hence, \\ 2^2+3^2\ne4^2 \\ It\text{ can not be the length of a right triangle} \end{gathered}[/tex]
Also,
[tex]\begin{gathered} 7^2+11^2=49+121=170 \\ 14^2=196 \\ Hence, \\ 7^2+11^2\ne14^2 \\ It\text{ can not be the length of a right triangle} \end{gathered}[/tex][tex]\begin{gathered} 8^2+10^2=64+100=164 \\ 12^2=144 \\ Hence, \\ 8^2+10^2\ne12^2 \\ It\text{ can not be the length of a right triangle} \end{gathered}[/tex]
Lastly,
[tex]\begin{gathered} 9^2+12^2=81+144=225 \\ 15^2=225 \\ Hence, \\ 9^2+12^2=15^2 \\ It\text{ can be the length of a right triangle because it follows the Pythagorean theorem} \end{gathered}[/tex]
Therefore, OPTION D is correct.
