Question

Find the length and width (with W < or equal to L ) of the rectangle with perimeter 72 that has maximum area, and then find the maximum area.

Answer 1

2W+2L=72
W+L=36
W=36-L
A=LW=L(36-L)
you want to find the vertex of the parabola A=L(36-L)
the x-coordinate is your length, y-coordinate is the maximum area

Answer 2

the easy way is to use a spreadsheet

the sum of length and width is 36

so start with a spreadsheet with columns

Width Length Area
1 35 35
2 34 78
3 33 99


repeat the process graph the points and you'll see a concave down
parabola.

the max area occurs when l = w = 18

or you can use differential calculus

Answer 3

Thank you! :)