Is A triangle with sides of lengths 12 15 and 20 a right triangle?

No. Pythagoras' theorem states that when the square of the hypotenuse is equal to the sum of the squares of the other two sides then it is a right-angled triangle. The hypotenuse is the longest side (opposite the supposed right angle).

In this case the hypotenuse is 20. The square of 20 is 400. The other two sides are 12 and 15. The square of 12 is 144 and the square of 15 is 225. The sum is therefore 225 + 144 = 369, which is not equal to 400, therefore the triangle cannot be a right-angled triangle.