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You have three fields, all square, so length = width.
Let x be the side length of the smallest square.
Then x+1 is the side length of another square.
And x+3 is the side length of the largest sqaure.
The area of the smallest square is x²
The area of the next square is (x+1)²
The area of the largest square is (x+3)²
Toatal sum of the fields areas is: A = x² + (x+1)² + (x+3)²
A = x² + x² + 2x + 1 + x² + 6x + 9
38 = 3x² + 8x + 10
3x² + 8x - 28 = 0
(3x + 14)(x - 2) = 0
x = -4 2/3, x = 2
Ignoring the negative side length,
x = 2 km
Area of field1 = 2² = 4 square kilometres
Area of field2 = 3² = 9 square kilometres
Area of field3 = 5² = 25 square kilometres