Solve the problem

Question

you have 84 feet of fencing to enclose a rectangular region. find the dimensions of the rectangle that maximize the enclosed area.

 

Solve problem involving a quadratic functions minimum or maximum value. 

Answer 1

P=2l+2w

84=2l+2w

42=l+w

42-w=l

A=lw

A=(42-w)(w)

A=42w-w²

use -b/2a

-42/2(-1)=-42/-2=21

you want a square 21 feet by 21 feet to maximize the area

A=21*21

A=441 square feet

try 20 feet by 22 feet

A=20*22

A=440 square feet

try 19 feet by 23 feet

A=19*23

A=437 square feet

the maximum area will always occur when the rectangle is a square