Find the dimensions and maximum area of a rectangle, if it’s perimeter is 24 inches

Perimeter = 24

triangle perimeter = 2W + 2L

24= 2W + 2L

12 = W + L

L= 12-W

AREA = W*L

AREA = (W)(12-W)
A = 12W-W^2
 
maximum occurs when you take the derivative 

d/dw=12-2w = 0 
w=6

after this i think we can say 6 * 6 = 36 is the maximum area.. not to sure, havent done a problem like this in a while

hope this helps 

or if we know what w=6 we can find L

L = 12-w which we still get 6