Question 151761
It can get confusing.
First name the sides of the fields.
How about S for small field, L for large field, and M for the middle field.
Since they're squares the area of each field is,
{{{A[S]=S^2}}}
{{{A[M]=M^2}}}
{{{A[L]=L^2}}}
The largest field side is 3 km larger than the small field.
{{{L=S+3}}}
One field is 1 kilometer longer than the side of the smallest field. 
I'm assuming this is the middle field.
{{{M=S+1}}}
The total area is 38 km^2.
{{{S^2+M^2+L^2=38}}}
Now substitute for M and L.
{{{S^2+M^2+L^2=38}}}
{{{S^2+(S+1)^2+(S+3)^2=38}}}
Note the expansion of the squares. 
Check on the FOIL method if this isn't clear.
{{{S^2+highlight(S^2+2S+1)+highlight(S^2+6S+9)=38}}}
{{{3S^2+8S+10=38}}}
{{{3S^2+8S-28=0}}}
You can factor this quadratic equation.
{{{(3S+14)(S-2)=0}}}
Two solutions:
{{{3S+14=0}}}
{{{S=-14/3}}}
A negative length does not make sense in this case so we throw out that answer.
{{{S-2=0}}}
{{{highlight(S=2)}}}
Then from above,
{{{M=S+1}}}
{{{M=2+1}}}
{{{highlight(M=3)}}}
and finally
{{{L=S+3}}}
{{{L=2+3}}}
{{{highlight(L=5)}}}
{{{A[S]=S^2=2^2=4}}}
{{{A[M]=M^2=3^2=9}}}
{{{A[L]=L^2=5^2=25}}}
The smallest field is 4 km^2, the middle field is 9 km^2, and the large field is 25 km^2.