I want to plant 600 plants that are spaced 3 feet apart with rows 3 feet apart

[MPRENO]

600 plants

3 feet apart

rows 3 feet apart

How much footage of land will i need to sufficiently plant all 600?

I've come up with varying answers and Im stumped.. Sometimes i come up with 25 sq ft but then I also came up with like 3,600 feet also and so I went out and used a tape measure and looked at 25 by 25 but it looks way too small for 600 plants that get about 5 to 6 foot tall on average.

Can someone please explain how to solve this and give me the correct answers?

 

[Deleted member 4993]

600 plants

3 feet apart

rows 3 feet apart

How much footage of land will i need to sufficiently plant all 600?

I've come up with varying answers and Im stumped.. Sometimes i come up with 25 sq ft but then I also came up with like 3,600 feet also and so I went out and used a tape measure and looked at 25 by 25 but it looks way too small for 600 plants that get about 5 to 6 foot tall on average.

Can someone please explain how to solve this and give me the correct answers?

Since you did not post the exact assignment - the answer can be One column of 600 plants placed 3 feet apart.

Did the problem state any term like "minimum" area in the description?​

​

Also include your work - e.g. how did you get 25 sqft. as your answer (by the way 25 ft. by 25 ft. would be 625 sq.ft)​

If you had included the original statement and work - you would have received significant assistance, by this time!!

 

[MPRENO]

Since you did not post the exact assignment - the answer can be One column of 600 plants placed 3 feet apart.

Did the problem state any term like "minimum" area in the description?​

​

Also include your work - e.g. how did you get 25 sqft. as your answer (by the way 25 ft. by 25 ft. would be 625 sq.ft)​

If you had included the original statement and work - you would have received significant assistance, by this time!!

I mean like in a square. I need to know how many rows I need and how many plants per row and how much footage I need of land... for 600 plants that must be space 3 feet apart going both width wise and length wise.

 

[Dr.Peterson]

I mean like in a square. I need to know how many rows I need and how many plants per row and how much footage I need of land... for 600 plants that must be space 3 feet apart going both width wise and length wise.

I take it this is not a classroom assignment, but a real-life question?

600 plants will not form a square! The square root of 600 is 24.5, so you'd round up to 25 rows of 25 plants (which allows for 625). Maybe that's how you got 25, but it isn't an area!

Now, how much space do you need for 25 rows, each holding 25 plants?

Alternatively, you could make a rectangle, e.g. 20 by 30 plants. Your problem statement allows for multiple solutions. (SK's 1 by 600 is one of them!)

 

[JeffM]

In fact, it is not clear what the question even is. It looks to me like a minimization problem in which each plant requires an area with a radius of three feet, and the plot must be a quadrilateral.

 

[MPRENO]

We're making progress☺

So yes thats how I got 25 and 25.. I need 3 feet of spacing in-between both every plant and every row. Thats how I got 75 by 75

Is that correct?

 

[Mr. Bland]

For any solution, each tree is regarded as a 3×3, or 9 square foot cell in a grid.

If the goal is to minimize area, any grid arrangement that exactly fits the 600 cells will yield the minimum of 5,400 square feet. Take all of the prime factors of 600 and partition them into two groups in any manner you like: 2, 2, 2, 3, 5, 5 as well as the special 1×600 case. Remember to multiply each dimension by 3 feet to yield the final physical dimension.

If the goal is to minimize perimeter, the plot should be as close to a square as possible, as a rectangle's perimeter will approach infinity the more dramatic the aspect ratio (provided its area remains the same). The number of cells on the longer dimension will be the square root of 600, rounded up. This is where 25 comes from, but remember that each cell is 3 feet on its own, so the dimension in feet is 75. The number of cells on the shorter dimension will be 600 divided by the number of cells on the longer dimension, rounded up. This works out to exactly 24 without rounding, which means it is also a minimum-area solution.

 

[MPRENO]

Right that all makes sense. Thanks so much! So I would need 25 feet by 24 feet?

Also... are you saying a square shape would take up less overall space (land) than a triangle or circle would? Cause I don't have much land to plant on and need the most efficient shape possible so I can plant more with less. Does shape matter at all?

 

[Dr.Peterson]

We're making progress☺

So yes thats how I got 25 and 25.. I need 3 feet of spacing in-between both every plant and every row. Thats how I got 75 by 75

Is that correct?

I don't see where you said 75 before, but yes.

Of course, what this means is that you have 3 feet between plants, and also 1.5 feet between outer plants and the fence around them, which makes sense.

As others have said, each plant is in the middle of a 3x3 square, so the total area actually taken up by plants is 600 times 9 = 5400 square feet, no matter how you arrange them; but assuming you want a square garden, you are forced to make a little extra space, making it 75 times 75 = 5625 square feet. (That is, you could fit 25 extra plants, which together would use up the extra 25*9=225 square feet inside the fence.)

As Mr. Bland said, you could instead make it 24 by 25 (= 600 plants exactly); this is 72 by 75 feet, or 5400 square feet exactly. In doing this, you are removing the last (empty) row of 25 plants from the square. If you don't mind it not being an exact square, that's presumably the best answer.

But you've never actually answered our questions about whether this is a formal exercise or a real-life problem, and what the actual constraints are in either case.

 

[MPRENO]

Its real life. I'm planting tobacco. So I assume 25 by 24 then is the best way to go. no outside spacing just in-between the plants only and no fence.

 

[Dr.Peterson]

Its real life. I'm planting tobacco. So I assume 25 by 24 then is the best way to go. no outside spacing just in-between the plants only and no fence.

What I mean by "fence" is the outer limit of the space "owned" in some sense by the plants.

If you think only about the space between the plants, then you will have 24 3' spaces one way and 23 3' spaces the other way, so the space in that sense (thinking of each plant as a point) will be 72' by 69'; but the plants themselves, not being mere poles, will extend some distance outside that (though probably not a full 1.5'). Thinking of each plant as taking up a 3x3 box makes it easier to think about.