The Pythagorean theorem proves a triangle is a right triangle if the square of the height plus the square of the base equals the square of the hypotenuse ( A^2 + b^2 = c^2) So the answers should be:
The Pythagoras Theorem is a^2 +b^2 = c^2 if this is true then you have a right triangle. So I think they are looking for side lengths in the first box.