Justin wants to use 168 ft of fencing to fence off the greatest possible rectangular area for a garden. What dimensions should he use? What will be the area of the garden?

A. 83x85; 7,055 ft^2
B. 50x34; 1,700 ft^2
C. 42x42; 1764 ft^2
D. 54x30; 1,620 ft^2

Question

Justin wants to use 168 ft of fencing to fence off the greatest possible rectangular area for a garden. What dimensions should he use? What will be the area of the garden?

A. 83x85; 7,055 ft^2
B. 50x34; 1,700 ft^2
C. 42x42; 1764 ft^2
D. 54x30; 1,620 ft^2

yanasidlinskiy · Answer

Quick hint: For all area optimization problems involving rectangles and varieties of rectangles, the optimization is ALWAYS a square. IE: Given a finite amount of material, the largest area it will enclose is always a square.

anonymous · Answer

So it is A?

yanasidlinskiy · Answer

No. The areas are already there on the right. Just find the largest one

anonymous · Answer

But the largest area is A.

anonymous · Answer

@YanaSidlinskiy please help me!!

yanasidlinskiy · Answer

Sorry @KimberlyAlice I was lost connection.. I'll just give it to you! It would be (C). Wouldn't it? The derivation of this would probably be helpful. Calculus?