A builder is designing a rectangular parking lot. She has 300 feet of fencing to enclose the parking lot around three sides.

Question

 What is the area of the parking lot.

Answer 1

you want maximum area I assume ???

P=l+2w

A=lw

300=l+2w

300-2w=l

A=(300-2w)(w)

A=300w-2w²

use -b/2a

-300/-4=75 feet for each width and 150 feet for the one length

the rectangle is 75 by 150 by 75

A=75*150=11,250 square feet for maximum area

if the dimensions were 74 by 152 by 74 the area would be 74*152=11,248 square feet which is less

if the dimensions were 76 by 148 by 76 the area would be 76*148=11,248 square feet again

maximum area is always a square and notice that two 75 by 75 squares make up the 75 by 150 by 75 rectangle