The other tutor assumed you meant "square" and not "rectangle".

This is worded very badly because there are two dimensions,
the larger getting larger as the smaller gets smaller.
You can't talk about "two things, both being the smallest",
and make any sense, when the shorter dimension, the
width, gets smaller, the length gets larger.

To show what I mean, look at these possibilities

                    P = 2L+2W    A = LW

 Length    Width    Perimeter    Area

   4        4         16         16
   6        3         18         18
   7        2.8       19.6       19.6
  10        2.5       25         25
  18        2.25      40.5       40.5
  20        2.222...  66.444...  66.444...  
  42        2.1       88.2       88.2
 402        2.01     808.02     808.02
4002        2.001   8008.002   8008.002     

Which of those has "the smallest possible dimensions"???
Notice that in all those cases the perimeter and area 
have the same numerical value.  The last one has the
smallest shorter dimension, but the largest longer
dimension.  Point this out to your teacher, because
the wording makes it impossible to know what is wanted.

[Notice that we have a pattern going there at the end, as 
the shorter dimension gets close to 2, the larger dimension
gets larger and larger and never stops getting larger.] 

Edwin