What type of graph is this? (in the picture) and how can these graphs be misleading?

It is a picture graph. It can be misleading if you dont know what each of the barrels are worth.

the answer would be the third option, "no, ariel should have added 9^2 and 12^2 and compared that to 15^2."

this is found through the pythagorean theorem, which is a^2 + b^2 = c^2.

this is the correct way of solving the problem:

9^2 + 12^2 = 15^2

81 + 144 = 225

225 = 225