If 1 acre of land is avalible, and each tree is 25 feet apart, how many trees can you fit in the acre of land?
+128731 Actually.....this is an interesting problem......
We can do better than 64 trees if we consider another configuration.....
Since the acre can be in any shape......consider one that is in the shape of an equilateral triangle
To find the side,S, of such a triangle, we can solve this:
43560 = [sqrt(3)S^2/4]
And S = about 317.7 ft on each side
Since the trees have to be 25 feet apart, it we plant the first one at the apex, we can actually plant
300/25 + 1 = 12 + 1 = 13 down each side .....there will be an "dead" space at the bottom of this triangle where no other trees can be planted with a 25 foot spacing requirement......
Then, theoretically, the number of trees that we could plant = [13*14] / 2 = 91
And, unlike a square planting area, each tree is guaranteed to be 25 ft from any of its "nearest neighbors"........[the diagonal neighbors in a square planting are sqrt(2)*25 ft apart....this "wasted" space is why we can't plant as many as in the equilateral configuration ]
Look at the picture of the first five rows :
Note that each tree is exactly 25 ft from any of its neighbors......!!!!
It would be interesting to see if another arrangement [such as a hexagonal one] would even be more productive.....!!!
If 1 acre of land is avalible, and each tree is 25 feet apart, how many trees can you fit in the acre of land?
1 square mile=640 acres
5280^2=640 acres,
1 acre=43,560 square feet
1acre=sqrt(43,560)
1acre=208.7^2 feet on each side
208.7/25=8.35 or 8 trees on one side, therefore,
8 X 8=64 trees, vertically and horizontally
+128731 Actually.....this is an interesting problem......
We can do better than 64 trees if we consider another configuration.....
Since the acre can be in any shape......consider one that is in the shape of an equilateral triangle
To find the side,S, of such a triangle, we can solve this:
43560 = [sqrt(3)S^2/4]
And S = about 317.7 ft on each side
Since the trees have to be 25 feet apart, it we plant the first one at the apex, we can actually plant
300/25 + 1 = 12 + 1 = 13 down each side .....there will be an "dead" space at the bottom of this triangle where no other trees can be planted with a 25 foot spacing requirement......
Then, theoretically, the number of trees that we could plant = [13*14] / 2 = 91
And, unlike a square planting area, each tree is guaranteed to be 25 ft from any of its "nearest neighbors"........[the diagonal neighbors in a square planting are sqrt(2)*25 ft apart....this "wasted" space is why we can't plant as many as in the equilateral configuration ]
Look at the picture of the first five rows :
Note that each tree is exactly 25 ft from any of its neighbors......!!!!
It would be interesting to see if another arrangement [such as a hexagonal one] would even be more productive.....!!!
+118613 If 1 acre of land is avalible, and each tree is 25 feet apart, how many trees can you fit in the acre of land?
How big is an acre? 43560 sqare feet according to our guest.
43560/25=1642.4
So if the land was 1 foot by 43560 feet and there was a tree up against one end of it then
I think 1643 trees would fit altogether. :/
