Answer:
[tex]A = 781250\,m^{2}[/tex], [tex]x = 625\,m[/tex], [tex]y = 1250\,m[/tex]
Step-by-step explanation:
The perimeter covered by the electric fence in meters is:
[tex]2\cdot x + y = 2500[/tex]
The area of the rectangle is:
[tex]A = x\cdot y[/tex]
[tex]A = x \cdot (2500-2\cdot x)[/tex]
Let differentiate the previous equation and equates to zero:
[tex]2500-4\cdot x = 0[/tex]
The critical point is:
[tex]x = 625\,m[/tex]
By the Second Derivative Text, it is proved that critical point lead to a maximum:
[tex]\frac{d^{2}A}{dx^{2}} = -4[/tex]
The other side of the rectangle is:
[tex]y = 1250\,m[/tex]
The largest area than can be enclosed is:
[tex]A = (625\,m)\cdot (1250\,m)[/tex]
[tex]A = 781250\,m^{2}[/tex]
The dimensions of the triangle are:
[tex]x = 625\,m[/tex]
[tex]y = 1250\,m[/tex]
