check the picture

The 2 adjacent rectangles (corrals) form one larger rectangle.

as shown in the figure, let x be the length of the fences perpendicular to the river, then the length of the side opposite to the river will be 420- 2x (yard)

so we can write the following function, which calculates the area A enclosed by the fence, as a function of x.

A(x)=2x(420-2x)

clearly A is a quadratic function, its graph is a parabola. This parabola looks downwards because of the minus of the term -2x

from A(x)=2x(420-2x) we can find that the x intercepts of the parabola are:

one of the roots is x=0

and

420-2x=0,

2x=420

x=210 is the other root.

The x coordinate of the vertex is the midpoint of (0, 210), that is 210/2=105

f(105)=2*105(420-2*105)=210*(420-210=2110*210=44,100 square yard.

the highest point of the parabola is the largest value the function takes, so the maximal area of the fence.

Answer: max area= 44,100 square yard.