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

Algebra ->  Square-cubic-other-roots -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
The tougher shape to analyze is the circle with the diameter.

r, the radius.
2pi%2Ar%2B2r=600
pi%2Ar%2Br=300
r%281%2Bpi%29=300
highlight_green%28r=300%2F%28pi%2B1%29%29-----radius for the circle.
Each run has almost then a max length of 600%2F%28pi%2B1%29=144%2Afeet, although the area might be more important.

The square shape with diagonal:
4x%2Bsqrt%282x%5E2%29=600
4x%2Bx%2Asqrt%282%29=600
x%284%2Bsqrt%282%29%29=600
highlight_green%28x=400%2F%284%2Bsqrt%282%29%29%29
As the value, x=73.9 feet.
The diagonal for this square is a length of 2%2Ax%5E2=2%2A%28400%2F%284%2Bsqrt%282%29%29%29
or diagonal is sqrt%282%2873.9%29%5E2%29=73.9%2A2=highlight_green%28147%29 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, pi%2Ar%5E2
Area Square, x%2Ax

Answer by MathTherapy(10552) About Me  (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: 16483.8%2F2, or highlight_green%288241.9%29 sq ft of space

Area of square pen: 12,280.94 sq ft, which means that each dog will have: 12280.94%2F2, or highlight_green%286140.47%29 sq ft of space

You decide which one should be built.