Is it possible to store a 20 foot long pipe in a rectangular room that is 10 feet by 12 feet by 8 feet?

First we'll consider the floor size.
In a 10 by 12 room the longest pipe that will fit lying on the floor equals the hypotenuse of a 10 by 12 triangle:
hypotenuse² = 10² + 12²
hypotenuse² = 100 + 144
hypotenuse² = 244
hypotenuse = 15.62 feet

Now we have to consider the third dimension (height = 8 feet).
The two sides would be 15.62 and 8
hypotenuse² = 15.62² + 8²
hypotenuse² = 244 + 64 = 308
hypotenuse = 17.55
So, the longest pipe that would fit in that room would be 17.55 feet long.