Answer:
largest area that can be enclosed = 8,000,000 m²
Step-by-step explanation:
Since it is a rectangle plot, the area is expressed as; A = xy, where x is length and y is width.
Because it is next to the river, he only needs to fence three sides, so amount of fencing; F = x + 2y.
Since we know the amount of fencing available is 8000m, we get:
8000 = x + 2y
solving for x, we have;
x = 8000 - 2y
substitute 8000 - 2y for x into the area equation to give;
A = (8000 - 2y)y distribute
A = -2y² + 8000y
Now, due to the negative sign next to 2, this will be a parabola which opens down, meaning that the point of maximum area will be at the vertex,
Thus; y = -b/2a = -8000/[2(-2)] = 2000
x = 8000 - 2(2000) = 4000
A = 4000(2000) = 8,000,000 m²
