Question

find the smallest perimeter and the dimensions for a rectangle with an area of 36 in^2

Answer 1

let "b" be the base
let "h" be the height

area of a rectangle = 36
A= b*h
36= b*h

Perimeter- want to minimize
P=2b+2h

substitute the area equation into the perimeter equation so you have perimeter in terms of only base or height

then find the derivative of the perimeter- set it equal to zero- solve for b or h (depending on which variable you substituted)- plug b or h back into the perimeter equation to determine minimum perimeter