measurement

To find the largest possible square that would fit into your garden, we would have to find the largest perfect square that will divide into 6912, which is the area of the garden. 256 is the largest perfect square to divide into 6912 and when you divide you get 27. This means that you could make 27 squares with equal areas that would fit inside your garden. Because a square's length and width are always the same, you just find the square root of 256 and you got your sides. So, 16 feet.

Walt:

To find the largest possible square that would fit into your garden, we would have to find the largest perfect square that will divide into 6912, which is the area of the garden. 256 is the largest perfect square to divide into 6912 and when you divide you get 27. This means that you could make 27 squares with equal areas that would fit inside your garden. Because a square's length and width are always the same, you just find the square root of 256 and you got your sides. So, 16 feet.

a garden measures 64 ft by 108 ft. the gardener wishes to subdivide the garden into congruent squares. what is the side length of the largest squares possible?

But Walt, 108 divided by 16 = 6.75 so there is not a 'whole' number of squares in the length.

For the moment, this question has got me stumped. I don't have a lot of time to think about it today, I definitely want to play with this question.

Sorry for the moment.
Melody.

Melody:

Walt:

To find the largest possible square that would fit into your garden, we would have to find the largest perfect square that will divide into 6912, which is the area of the garden. 256 is the largest perfect square to divide into 6912 and when you divide you get 27. This means that you could make 27 squares with equal areas that would fit inside your garden. Because a square's length and width are always the same, you just find the square root of 256 and you got your sides. So, 16 feet.

a garden measures 64 ft by 108 ft. the gardener wishes to subdivide the garden into congruent squares. what is the side length of the largest squares possible?

But Walt, 108 divided by 16 = 6.75 so there is not a 'whole' number of squares in the length.

For the moment, this question has got me stumped. I don't have a lot of time to think about it today, I definitely want to play with this question.

Sorry for the moment.
Melody.

Good point Melody, I failed to see this. Ok so I think this is the right way,
To find the side lengths of the largest possible squares then you would have to find the greatest common factor of both 64 and 108 which is 4. Here is the why:

Another way to look at the length and width of this rectangle is that it tells you that you could fit 64x108 tiny boxes, all with side lengths of 1, inside the rectangle. If the side lengths of your overall rectangle have a common factor that means you could group up the little unit boxes into bigger ones. The biggest boxes you could possibly group them into will have side lengths of your greatest common factor which in this case is 4. If you draw yourself a picture in your head you'll see how it all works out.

Excellent work Walt.

I did think of this answer yesterday but I had a little nagging doubt in my brain. I don't think that doubt was justified.
I believe your answer is completely correct.

I'll tell you what I was thinking.
Why does the smallest common factor of 2 whole numbers have to be a whole number?
I think it does, I can't think of any example where it is not, but, this question just got me thinking about it.