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

The mode of the numbers is 29.