A farmer wants to enclose a rectangular field with 180m of fencing. The side of the barn will act as one side of the enclosure, leaving 3 sides to be covered. The function that describes the area inside is f(x)=x(180-2x) what are the dimensions of the closure with the largest area?

Answer 1

180 x - 2 x^2 = A

2 x^2 -180 x = -A

x^2 - 90 x = - A/2

x^2 - 90 x + 45^2 = -A/2 + 45^2

(x-45)^2 = -(1/2) (A- 4050)

vertex at x = 45
so 45. 45 , 90
area = 4050

Answer 2

Thanks Damon! We got it now. We were stuck after line three so this was helpful.

Answer 3

Good, you are welcome