Atriangle has sides of lengths 10 24 and 26 is it a right triangle explain?

Yes.  For right triangles, the sum of the squares of the shorter sides is equal to the square of the longer side.  Thus, this is a right triangle if 10^2+24^2=26^2.  Expanding these squares, we have 100+576=676, which is true.  Thus, the triangle is right.

   c² = a² + b²
 26² = 10² + 24²
676 = 100 + 576
676 = 676

It is a right triangle because it shows that it has the same answer of the Pythagorean equation.