Question

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.

(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