Question

if you were given a rectangle with a certain area, how would you draw it so that it had the greatest perimeter?

Answer 1

we know

A------------------> area of rectangle

Let
x-----------> larger side
y-----------> smaller side
r------------> ratio

r=x/y
we know that
if r=1----------- > is a square

to get the largest perimeter I would draw it increasing its larger side x and decreasing its smaller side y, keeping the same area
the ratio must be r>1

example 1
if you have two rectangles with the same Area
the rectangle A have r=1.6 and the rectangle B have r=3
the perimeter of rectangle B > perimeter of rectangle A

example 2
the area of rectangle is 6 units²
rectangle 1-------> 3x2
r=3/2=1.5
P=10 unit
rectangle 2-------> 6x1
r=6/1=6
P=14 units