Respuesta :
Answer:
The maximum possible area of the pasture is 26,450 feet square.
Step-by-step explanation:
Let us assume the width of the rectangular area = m ft
and the length of the area = k ft
Also assume: ( one side with k units IS NOT FENCED)
So, the total perimeter of the fencing is:
2 m + k = 460
or, k = 460 - 2m ........ (1)
Now, AREA OF THE RECTANGULAR PORTION = Length x Width = k x m
Put k = 460 - 2m
We get: A = m (460 - 2m)
or, A = 460 m - 2m²
We need to find the maximum for the parabolic function A = 460 m - 2m²
The function has a maximum value as the quotient in front of x^2 is negative: -2 < 0
A (max) = [tex]c-\frac{b^2}{4a}[/tex] where a = -2, b = 460, c = 0
= [tex]-\frac{(460)^2}{4(-2)} = 26,450[/tex]
A max = 26,450 sq ft.
The maximum possible area of the pasture is 26,450 feet square.
