If PQ=21 cm and QR=5cm, then what are the possible lengths for PR so that line PQ, line QR, and line PR can form a triangle? explain your reasoning

I have a pretty good idea what the answer is i just need it explained a smidge more.

We know that PQ is 21 cm and QR is 5 cm. There are only 2 possible answer for this and you use only one formula. It's called the Pythagorean theorem.

The first possible is this. If the hypotenuse (the longest side of a triangle) is PR, we do:

a² + b² = c² ←Fill in the numbers

21² + 5² = c²

441 + 25 = c²

466 = c²

√466 = 21.12 cm←Possible length

The second possible is this:

5² + b² = 21²

25 + b² = 441

b² = 441 - 25

b² = 416

√416 = 20.4←Another possible answer