The length of sides of a right triangle always satisfy the pythagoras theorem.
Apply the pythagoras theorem to each sides of triangle.
[tex]\begin{gathered} (63)^2=(31)^2+(32)^2 \\ 3969=961+1024 \\ 3969\ne1985 \end{gathered}[/tex]
Length of sides not belong to a right triangle.
For second option,
[tex]\begin{gathered} (53)^2=(28)^2+(45)^2 \\ 2809=784+2025 \\ 2809=2809 \end{gathered}[/tex]
Pythagoras theorem satisfied. Sides belongs to a right triangle.
Third option,
[tex]\begin{gathered} (64)^2=(36)^2+(49)^2 \\ 4096=1296+2401 \\ 4096\ne3697 \end{gathered}[/tex]
Sides not belongs to a right triangle.
Fouth option,
[tex]\begin{gathered} (169)^2=(5)^2+(12)^2 \\ 28561=25+144 \\ 28561\ne169 \end{gathered}[/tex]
Sides not belong to a right triangle.
So possible length of a right triangle is 28, 45, 53.
