Question

Find the length and width of a rectangle with maximum area that has a perimeter of (5P) units.

Answer 1

perimeter of a rectangle = what?
area of a rectangle = what?

Answer 2

Perimeter = 2L + 2W
Area = LW

Answer 3

so you're trying to maximize area
5P=2L+2W
solve for a variable
2L=5-2W
L=5/2-W
substitute it into area
(5/2-W)(W)
distribute
5W/2-W^2=A
take the derivative to find critical points
A'=5/2-2W
Set = to 0
0=5/2-2w
-5/2=-2w
w=5/4
plug back in to perimeter
5=10/4+2L
10/4=2L
L=5/4
so the maximum area would be when L=5/4 and W=5/4
which is 1.5625

Answer 4

basically here's how to optimize
you're given a primary equation (you want to optimize it) and a secondary equation (you use it strictly to help you solve the problem, you don't need to find the maximum or anything)
obviously the primary in this case is area
1. identify the 2 equations
2. identify which is primary and which is secondary
3. solve for a variable using the secondary
4. substitute back into primary
5. take derivative
6. set = to 0 (finding critical points)
7. plug 1 solved variable back into the original equation to find the other
8. plug both back into the original equation to find maximum

Answer 5

The part where you solved for the variable, you eliminated P? I %P the whole figure or just 5?

Answer 6

Is 5P***

Answer 7

yeah because I assumed P was just to tell you the perimeter
if it's another variable there's no way you can solve (I think)