Answer: Maximum Area of the field is 5625m²
Step-by-step explanation: If one side is a river, there is no need to fence this side. So, calling the sides of the retangule x and y, we know that the perimeter of the fence is the sum of all sides that will have the fence, so, 2x+y = 150.
We want maximum area, and area is xy
A = xy
2x + y = 150
y = 150 - 2x
A = x(150 - 2x)
To find the maximum area, we need de vertex of this parabola.
x(150 - 2x) = 0
150x - 2x² = 0
75x - x² = 0
a=-1 b=75 c=0
For the vertex: Vy = -Δ/4a
Δ = b² - 4ac = 75² - 4.-1.0 = 75² = 5625
Vy = -Δ/4a = -5625/4.(-1) = 5625