Given a rectangle with a perimeter of 24 inches, why dimensions maximize the area?

The dimensions are 6 by 6

Step-by-step explanation:

Calculus

2x +2y= 24

xy= A

2x=24-2y

x=12-y

(12-y)(y)= 12y- y^2

the Derivative is = 12-2y

Then set that equal to zero 0=12-2y

-12=-2y

y=6

Confirm that 6 is a maximum by using a wiggle graph

wiggle graph -∞<---inc--6---dec-->∞

6 is a maximum

plug into original equation

2x + 2(6)=24

2x+12=24

2x=12

x=6

y=6

x=6

4n=2m

ratio of m to n: 2/4 = 1/2

answer

a. 1/2