Question
Optimization: Of all rectangles with perimeter P , the one with the largest area is a square of side length P/4.
True or False and explain reasoning
True or False and explain reasoning
Answers
Steve
true
If the perimeter is p, then
2x+2y = p
y = (p-2x)/2 = p/2 - x
The area is
a = xy = x(p/2-x) = p/2 x - x^2
This is just a parabola, with vertex at x = p/4
so, y = p/4 as well,
and you have a square to get max area.
If the perimeter is p, then
2x+2y = p
y = (p-2x)/2 = p/2 - x
The area is
a = xy = x(p/2-x) = p/2 x - x^2
This is just a parabola, with vertex at x = p/4
so, y = p/4 as well,
and you have a square to get max area.