SOLUTION: I am building a fence to keep two dogs separated. I have 600 feet of fence. I can build a circular pen, which I will divide with a diameter giving each dog the equal amount of spac

Question 971355: I am building a fence to keep two dogs separated. I have 600 feet of fence. I can build a circular pen, which I will divide with a diameter giving each dog the equal amount of space or I can build a square pen and divide it diagonally giving each dog equal space. Show the solution of each formation and provide a labeled diagram and the algebra leading to the solution and determine which fence I should build
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
The tougher shape to analyze is the circle with the diameter.

r, the radius.

-----radius for the circle.
Each run has almost then a max length of , although the area might be more important.

The square shape with diagonal:

As the value, feet.
The diagonal for this square is a length of
or diagonal is point something feet.

Which shape for the 600 foot length of material depends on single dimensional length is important or if area is important. The circle shape, being near the value of the square's diagonal, might be better because of how the curve occurs near the ends of the diameter.

Area Circle,
Area Square,
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

I am building a fence to keep two dogs separated. I have 600 feet of fence. I can build a circular pen, which I will divide with a diameter giving each dog the equal amount of space or I can build a square pen and divide it diagonally giving each dog equal space. Show the solution of each formation and provide a labeled diagram and the algebra leading to the solution and determine which fence I should build

Area of circular pen: 16,483.8 sq ft, which means that each dog will have: , or sq ft of space
Area of square pen: 12,280.94 sq ft, which means that each dog will have: , or sq ft of space
You decide which one should be built.
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