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Since EP  =  FP   and  GQ  = FQ   we  have  this system

4y + 2  =  2x     ⇒   2y + 1   =  x

4y +4  =  3x - 1

Sub the first equation into the second  for x  and we have that

4y + 4  =  3(2y+1) - 1

4y + 4  = 6y + 2        rearrange as

2 = 2y

1 = y

And 2(1) + 1  =  x  = 3

Since PQ  is a median, then  EG =   2 ( x + 2y)  =  2 ( 3 + 2*1)  = 3 ( 5) = 15

So.......the perimeter  is

4y + 2   + 2x  + 4y + 4 + 3x - 1  + 15   =

4(1) + 2 + 2(3) + 4(1) + 4 + 3(3) - 1 + 15  =

4 + 2 + 6 + 4 + 4 + 9 - 1   + 15  =

43