Question 161327
Find the length of the side on each field.
Let X be the length of the smallest field.
You are told the second field has a side length 1 kilo longer. So its side is (X+1)
You are also told the third field has a side length of (X+3)

The area of a square is given by {{{A = s^2}}} where s is the length of one side
The total area of all 3 fields is given as 38 Km^2. 

All we need to do now is add the three fields and then solve for X
{{{TotalArea = Area1 + Area2 + Area3}}}
{{{38 = X^2 + (X+1)^2 + (X+3)^2 }}}
{{{38 = X^2 + (X^2 + 2X +1) + (X^2 + 6X + 9)}}}
{{{38 = 3X^2 + 8X + 10 }}}
{{{0 = 3X^2 + 8X - 28}}}
{{{0 = (3X + 14)(X - 2)}}}

So either {{{3x+14 = 0}}} or {{{X-2 = 0}}}
Thus either {{{x = -14/3}}} or {{{X=2}}}
Since the length cannot be negative, the answer must be 2.

The small field is 2x2, the middle one is 3x3 and the largest one is 5x5. 
Is 4 + 9 + 25 = 38?