A rectangular box has a perimeter of 50 inches. Find the length and width of the box that would give the maximum area. Find the maximum possible area of the box.

Answer 1

square :)
side = 50/4 = 25/2

A = x y
P = 2x+2y = 50
so y = (25-x)
A = x(25-x) = 25 x - x^2

x^2 -25 x = -A
x^2 - 25 x + (25/2)^2 = -A + 625/4

x = 25/2 sure enough so y = 25/2
and A = 625/4 = (25/2)^2

Answer 2

I'm random.
I think the answer is 12.5 inches but this problem is probably way harder than I thought lol