Posted by Mathlete on .
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(1802x) what are the dimensions of the closure with the largest area?

Functions 
Damon,
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
(x45)^2 = (1/2) (A 4050)
vertex at x = 45
so 45. 45 , 90
area = 4050 
Functions 
Mathlete,
Thanks Damon! We got it now. We were stuck after line three so this was helpful.

Functions 
Damon,
Good, you are welcome