Let's say that the rectangle has length of x and width of y. That means the perimeter is 2x + 2y = 1400.
We also know that the ratio of the width to the length is 3:4 which means y/x = 3/4.
This is now a system of equations with 2 equations and 2 unknowns.
To solve, we start by rearranging the second equation giving us y = 3x/4.
We then replace all the y in the first equation by substituting the second equation into the first one wherever we see y:
2x + 2(3x/4) = 1400
This gives us an equation with only x as the unknown which we can solve:
2x + 2(3x/4) = 2x + 3x/2 = 3.5x = 1400
x = 1400/3.5 = 400 <- this is the length.
Since we know that x = 400, we can now substitute this value back into the second equation to solve for y:
y = 3x/4 = 3(400)/4 = 300.
The field's dimensions are 300m x 400m.