Partition a stable (Middle School Math)

Question

Middle School Math Club Question :
The stable, $6$ yards by $6$ yards with concrete walls, is divided by internal wooden partitions into stalls $1$ yard by $2$ yards.
What could be the total length of the wooden partitions? Find all possible answers.

My daughter had this question at her Math Club. There is no mention of thickness of the wooden partitions. So she is a tad confused on this.

Answer 1

"My daughter had this question .... she is a tad confused on this."

It is not her fault : I too am confused , because that Question is almost meaningless.

(1) When the Stable has concrete walls , how can the horses enter & leave ?
(2) Even if we can assume some gate (where ? what length ?) , then should we tightly pack the Stalls & horses , leaving no corridor or way or room for horses to walk in ?

[[ We generally take Partitions to have theoretically Zero thickness , which is Practically negligible thickness ]]

With those caveats , here is a "straight-forward" way to get "some" answer ....

Area of Stable is $6 \times 6 = 36$
Perimeter of Stable is $6 + 6 + 6 + 6 = 6 \times 4 = 24$

Area of Stall is $1 \times 2 = 2$
Perimeter of Stall is $1 + 2 + 1 + 2 = 2 ( 1 + 2 ) = 6$

Within that Stable Area , we can have $36 / 2 = 18$ Stalls , with no space or aisle or way to enter & leave.

That will require $18 \times 6 = 108$ Wooden Partition length.
We do not require Partition where there is a wall , hence we can exclude that :
$108-24=84$ Partition length

This is Double Counting the Internal Partitions , where-ever two Stalls have Common Partition.
Hence we should take half :
$84/2=42$ Partitions

Thus $42$ is the Maximum Partition length we will ever require. When we have aisles , corridors or ways to enter , we will have fewer Stalls & we will require lesser Partitions ....

A BETTER WAY TO WORD THE QUESTION

Avoiding all the meaninglessness , we can make the Equivalent Question like this :
We have a $6 \times 6$ Square.
Draw $1 \times 2$ Dominoes inside it.
Maximize the Number of Dominoes.
We want to know the total length of lines involved.

Answer : 42

Answer 2

First divide the total area into nine 2*2 yard squares using two vertical dividers and two horizontal dividers of 6 yards each giving a sub total of 24 yards.

9 square cubicles each require a 2 yard sub-partition = +18 yards.
Orientation of sub partitions does not matter.

Total yardage of wooden partitions = 24+18 = 42 yards.

P.S. Lifts will have to be installed to get the horses in and out.

Alternatively, using a method similar to the one suggested by JAAP in the comments:

First divide the total area into 36 squares of 1 yard by 1 yard using 5 vertical and 5 horizontal dividers of 6 yards each adding up to 5 * 2 * 6 = 60 yards.

Now remove 18 sections of 1 yard each and the total required yardage is 60-18 = 42 yards. This covers all possible permutations of dividing the stalls up.