Atriangle has side lengths of 7, 10, and 12. is the triangle a right triangle

In a right-triangle, the sum of squares of the short sides equals the square of the long side (Pythagoras theorem).
7^2+10^2=49+100=149
12^2=144

Since the sum of squares of the short sides does NOT equal the square of the long side, the triangle is not a right triangle.