Is it possible to have a 150cm side, 10cm side and another 10cm side on a have been stuck on this for a while so me answer it

No.
To have a triangle, the two short sides must be longer than the long side, otherwise the two short sides will not touch.
Imagine you have three pencils, one long one and two short ones. Normally, you could make a triangle by touching each pencil end to another. But, if the two short ones are too short, then no matter how you angle the pencils, the ends will not touch (as shown in the image). 

2. root 6 is the right answer