Do the following lengths form a right triangle?

21) Yes; 23) Yes

Step-by-step explanation:

If the lengths form a right triangle, the sum of the squares of the two shorter sides should equal the square of the longest side (Pythagoras).

21)

5² +  12² =  13²

25 + 144 = 169

       169 = 169

The lengths form a right triangle.

23)

3² +  4² =  5²

9  + 16 = 25

      25 = 25

The lengths form a right triangle.