Answer:
 x = 77 ft; y = 14 ft
Step-by-step explanation:
We assume that "adjoining squares" means the small square shares a side with the large square, so the total length (in feet) of fence required for the enclosure is ...
 4x +3y = 350
The sum of the two areas is 6125 ft², so we have another relation:
 x² +y² = 6125
We can use the first equation to write an expression for y, then substitute that into the second equation. The result is a quadratic in x.
 3y = 350 -4x
 y = (350 -4x)/3
Then ...
 x² + ((350 -4x)/3)² = 6125 . . . substitute for y
 9x² +(350 -4x)² = 55125 . . . . multiply by 9
 25x² -2800x +67375 = 0 . . . . subtract 55125 and simplify
 x² -112x +2695 = 0
 (x -35)(x -77) = 0
This has two solutions: x = 35 and x = 77. We know that the square of sides x must use more than half the fence, so it must have side lengths greater than ...
 (350/2)/4 = 43.75 . . . . feet
The appropriate choice for x is 77 feet. Then ...
 y = (350 -4x)/3 = 42/3 = 14 . . . feet
x and y are 77 feet and 14 feet, respectively.
