A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 308 feet of fencing, what is the largest area that can be enclosed? Please explain how you got your answer :)

Question

anonymous · Answer

If he has 308 feet of fencing, that means the highest possible perimeter would be 308 feet.  So the equation would be: $$308=2L+2W$$
Division property of equality gets: $$154=L+W$$
Area of a Rectangle:$$A=LW$$
The highest possible area would be if it was a square, with two sides of 77.  So the highest possible area would be 5929 square feet.

Hope that helped.

anonymous · Answer

Thankyou so much!

anonymous · Answer

Quick question.. Why is the highest possible area a square??

anonymous · Answer

I know this is late cuz I logged off, but to be honest I couldn't tell you.  I've just come to accept it since using a calculator supports it.  Try 77 x 77.  Then 76 x 78.  And so on.  The farther apart the numbers are, the smaller the area.  idk why.