Among all rectangles that have a perimeter of 28, find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.

Answer 1

28/4 = 7

dimensions are 7 by 7, with area = 49

which is the maximum possible area if perimeter = 28

a square gives maximum area for a given perimeter

6 by 8 has area = 48

5 by 9 has area =45

4 by 10 has area = 40

the larger the difference in width and length, the smaller the area. the closer width and length are the larger the area.

this could also be a calculus problem

Perimeter = 2(L+W) = 28

L+W = 14

L = 14-W

Area = A = LW = (14-W)(W)= 14W -W^2

take the derivative and set equal to zero

A' = 14-2W = 0

2W = 14

W = 7 wide

L =14-7 = 7 long