Question 98207
If the side of the small field is x then the next field will have a side of (x+1) and the last field has a side length of (x+3).

The total area of the three square fields will be
{{{x^2+(x+1)^2+(x+3)^2}}}
{{{x^2+x^2+2x+1+x^2+6x+9}}}
{{{3x^2+8x+10}}}
This is equal to the total area of 38 so
{{{3x^2+8x+10=38}}}
{{{3x^2+8x-28=0}}}
Factorise
{{{(x-2)(3x+14)=0}}}
so x=2 or x=-4 2/3
Only a positive value makes sense
so the fields have a side length of 2, 3 and 5.
A check of these values shows the total area = 4 + 9 +25 = 38.