find the length and width of a rectangle

Question

Find the length and width of a rectangle that has the given perimeter and a maximum area.

Perimeter: 20 meters

Length?

Width?

Please provide how u got the answer along with the answer because I keep messing up.

Answer 1

20/4=5

maximum area = 5^2 = 25

Length = 5

Width = 5

a square has maximum area for a quadrilateral of fixed perimeter

A = LW

2L + 2W = 20

L+W = 10

L= 10-W

or solve with a little calculus

A = (10-W)W = 10W -W^2

take the derivative and set =0

A' = 10 -2W =0

2W = 10

W =10/2 = 5 = Width

L=10-W = 10-5 = 5 = Length

Maximum Area = 5 x 5 = 25