Out of all possible rectangles with a perimeter of 600, what should the size of two of its sides be, in order for that rectangle's area to be maximal?

Question

I only need the smaller side of the rectangle!!

Answer 1

Let x be the length and y the width

2x + 2y = 600

So, y = 300 - x

Area = A = x(300 - x) = -x² + 300x

The graph of the area function is a parabola opening downward.

The highest point on the graph occurs at the vertex of the parabola, which has x-coordinate

x = -300 / (2(-1)) = 150.

So, x = y = 150. (The rectangle with largest area is a square)

Answer 2

The rectangle of maximum area is a square!

Answer 3