Question

Find the smallest perimeter and the dimensions for a rectangle with an area of 225 in^2

Answer 1

To solve this, let the dimensions be x and y. We know that the area is 225. So, x * y = 225

Let the perimeter be denoted as P.

P = 2x + 2y

sine y = 225/x

P = 2x + 450/x

P' = 2 - 450/x^2

P'' = + 900/x^3

Put P' = 0

then x = 15

at x =15 P'' is positive

So the minimum perimeter, will be:
P = 2 (15 + 15) = 60 cm