SOLUTION: As a real estate tycoon you have bought a rectangular parcel of waterfront property and want to enclose your land as follows: Using 5000 feet of fencing you want to enclose a rect

Question 162778: As a real estate tycoon you have bought a rectangular parcel of waterfront property and want to enclose your land as follows: Using 5000 feet of fencing you want to enclose a rectangular section on only three sides using the water as the 4th side. What dimensions (length and width of the rectangle) should the enclosure be to assure maximum area?
I have been working on this problem for over two hours, it's ripping my mind apart! PLEASE HELP.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
THE MAXIMUM AREA FOR A FENCE AROUND 3 SIDES OF A RECTANGLE IS:
1*1*2=4 EQUAL MEASUREMENTS.
5,000/4=1250 FT.
SO YOU'LL HAVE 2 SIDES=1,250 EACH & 1 SIDE=2*1,250 OR 2,500 FT.
1,250+1,250+2,500=5,000 FT. OF FENCING.
1,250*2,500=3,125,000 FT^2 IS THE MAXIMUM AREA ENCLOSED.
PROOF:
REDUCE EAACH OF THE TWO 1,250 FT. FENCES BY 1 FOOT & INCREASE THE 2,500 FT FENCE BY 2 FT.
1,249*2,502=3,124,998 FT^2.
OR DECREASE THE 2,500 FT FENCE BY 1 FT & INCREASE EACH OF THE 1,250 FT FENCES BY 0.5 FT.
2,499*1,250.5=3,124,999 FT^2.
RELATED QUESTIONS
Hi, Could you please help me solve the below problem. Much appreciate your help. Thank... (answered by richwmiller,MathTherapy)

You own a piece of land on which you owe the bank $12,760 to the bank. You decide to... (answered by checkley77)

You, as a real estate agent, sell a property for $230,000. If you earn a 5% commission,... (answered by tommyt3rd)

Two Population Means A tomato farmer with a very large farm of approximately 2200... (answered by Boreal)

1. You are given 200 ft of fencing to enclose a rectangular garden plot. You can... (answered by Alan3354)

A triangular parcel of land has the border lengths of {{{ 55 }}} meters, {{{ 85 }}}... (answered by ikleyn)

You have 96 feet of fencing to enclose a rectangular pen for your dog. To provide... (answered by rfer)

Land and Sea Corporation has just purchased some shoreline property, and according to... (answered by josmiceli)

You have 700 feet of fencing to enclose a rectangular field. Express the area of the... (answered by drk)