You have to find the common denominator, in this case it would be 12. Then you multiply the denominator to get 12... then whatever you do to the top you must do to the bottom. Then, you add 7+2 and the fractions. This mixed number cannot be simplified.
The student is correct. Due to the meaning of perimeter which is all sides added up to make a number total, it is possible for a square and a rectangle to have the same perimeter if the numbers add up.