geom. word prob.: Find width, length of kennel, given....

[helpme100]

A resort owner has 104 ft of 6 ft tall chain link fence and she wants to make a dog kennel for boarding guest's dogs. If the kennel is to be 3 times as long as it is wide and it is to be divided into six equal areas by running fences parallel to the width, find the width and length of the kennel.

 

[tkhunny]

1) Notice that we do not need to know how tall the fence is.
2) Draw a picture. It will take two short ends and to long sides AND FIVE internal fences the same length as the long sides. Why?
3) Add all that up and ...
4) have you used your clue? length = 3*width

 

[soroban]

Re: geom. word prob.: Find width, length of kennel, given...

Hello, helpme100!

Did you make a sketch?

A resort owner has 104 ft of 6 ft tall chain link fence
and she wants to make a dog kennel for boarding guest's dogs.
If the kennel is to be 3 times as long as it is wide
and it is to be divided into six equal areas by running fences parallel to the width,
find the width and length of the kennel.

      : - - - - - - - - 3x- - - - - - - - :
      *-----*-----*-----*-----*-----*-----*
      |     |     |     |     |     |     |
     x|    x|    x|    x|     |x    |x    | x
      |     |     |     |     |     |     |
      *-----*-----*-----*-----*-----*-----*
      : - - - - - - - - 3x- - - - - - - - :

Let \(\displaystyle x\) = width.
Let \(\displaystyle 3x\) = length.

There are 2 lengths of fencing which are \(\displaystyle 3x\) feet long
. . and 7 lengths which are \(\displaystyle x\) feet long.
Hence, the total fencing is: \(\displaystyle \,2(3x)\,+\,7(x)\:=\:13x\) feet.

Since there is 104 feet of fencing: \(\displaystyle \:13x\:=\:108\;\;\Rightarrow\;\;x\,=\,8\)

Therefore, the kenncel will be \(\displaystyle 8\) feet wide and \(\displaystyle 24\) feet long.