A rectangular lot is bordered on one side by a stream and on the other three sides by 360m of fencing. Find the dimensions of the lot in order to maximize area.

Question

(Also, does it make sense if the answer I got is 180m width, 90m length?)

Answer 1

So, we will assume there is no need for a fence along the stream.

let the side parallel to the stream be y m
let each of the other two sides be x m
so 2x + y = 360
y = 360-2x

area = xy = x(360-2x)
= -2x^2 + 360x

the vertex of this parabola produces a maximum
the x of the vertex is -b/(2a) = -360/-4 = 90
if x = 90 , then y = 360-2(90) = 180

You are correct