Thread: Dimensions of Dog Pen

You wish to build a rectangular pen for your dog with 24 yards of fence. What are the dimensions (length and width) of the pen that will allow for maximum room to roam?

Is there a way to solve this question without using a graphing calculator or calculus?

Our teacher used a graphing calculator and found the maximum point to be (6,36) where the number 6 = the length and 36 = the width wirtten (L, W).

That's find and dandy but how does answer this question without a calculator and without calculus?

Originally Posted by magentarita

You wish to build a rectangular pen for your dog with 24 yards of fence. What are the dimensions (length and width) of the pen that will allow for maximum room to roam?

Is there a way to solve this question without using a graphing calculator or calculus?

Our teacher used a graphing calculator and found the maximum point to be (6,36) where the number 6 = the length and 36 = the width wirtten (L, W).

That's find and dandy but how does answer this question without a calculator and without calculus?

Yes there is another way to solve this by making perfect square (completing the square)

Let length of rectangular pen is x
and width of rectangular pen is y.

Perimeter







Now Area







So, the maximum area is 36 when x = 6 m, so that y = 12 - 6 = 6 m.

Originally Posted by Shyam

Yes there is another way to solve this by making perfect square (completing the square)

Let length of rectangular pen is x
and width of rectangular pen is y.

Perimeter







Now Area







So, the maximum area is 36 when x = 6 m, so that y = 12 - 6 = 6 m.

I knew there was another way.

Thanks