Figure A Figure B
Which of the triangles in the two figures above is a right triangle? Explain your choice using
the Pythagorean Theorem to prove it. Note: the figures are not drawn to seale.

Figure B

The Pythagorean Theorem is , where c is the longest side of the triangle (the hypotenuse).

To find the side length of each square, you have to square root the area of each square. This means that Figure A has side lengths of 3, 6 and 8 units. Figure B has side lengths of 5, 12 and 13 units.

In Figure A, if the triangle is right-angled, the equation must be correct. 9 + 36 = 45. 45 is not equal to 64, so the triangle is not right-angled.

In Figure B,  if the triangle is right-angled, the equation must be correct. 25 + 144 = 169. 169 is 13 squared, so the triangle is right-angled.

Alternatively, as you are already given the square values for each side length, there is no need to square root and square again. You can just test if the two smaller areas equal the larger area, but the explanation above uses a more detailed example of the Pythagorean Theorem.