Thread: Am I going nuts?

This problem doesn't seem to make sense based on the context of the problem.

Jordan wants to fill a square flower bed with 24 perennials. The landscaper recommends that he allow 1.5 square ft per plant. What should the length of one side of the flower bed be.




Now squares have all equal sides. 24 is not a perfect square. So how are you to fill a square flower bed with 24 flowers without there being a gap somewhere. Am I nuts or is this problem not possible given the context?

The only thing I can think of is a 5x5 with the middle space empty. But then that to me doesn't fulfill the part of the problem where it says FILL the flower bed with 24 perennials. Unless it is typical of flower beds to have a gap in the middle?

At first glance, we have (24 plants) * (1.5 ft^2 / plant) = 36 ft^2. So... 6x6 ??

[edit]

Had a dumb moment there.

I cannot speak for whether or not you are nuts but the fact that 24 is not a perfect square is not at all relevant to this problem for two reasons. First, 24 is the number of plants, not an area. To "allow 1.5 square ft per plant", the 24 plants will take 24*(1.5)= 36 square feet which is a perfect square. But even if it weren't the length of a side does NOT have to be an integer number of feet.

Originally Posted by Jman115

If you have a 6x6 then you only have enough room for 4 plants in each row and in each column which is only enough for 16 plants.


And if you do 6 plants x 6 plants then you have a hole in the middle which would not technically be a square? And if you wanted to call it a square it is not filled.

NO! "1.5 square feet" does not mean 1.5 feet on a side! A square with area 1.5 has each side of length 1.22 (approx) feet. 6/1.22 is slightly less than 5 plants per row or column.

I understand that 36 sqft is a perfect square and that is the area these plants take up. But if each side was 6 ft long then you would have 4.89897 flowers per side. You cannot put PART of a flower in a space. That is why i said based on context this seems impossible.

Unless some flowers take up a rectangular area, while others are taking up squares. But that seems an odd thing to do. You would think each flowers area would need to be a specific shape. I am assuming these flowers need space to grow in all directions so that is why I assume each flower needs to be inside a square and not a rectangle so they don't start growing into one another.

And yeah I know 1.5 sqft means that I just had a dumb moment there.

i see no reason why 4 rows of flowers spaced 1.5 feet apart, with the flowers in each row spaced 1 foot apart (6 per row), would not satisfy the problem

(or 6 rows spaced 1 foot apart, with 4 flowers in each row spaced 1.5 feet apart, if you prefer). the space allotted to each flower is then 1.5 square feet.

Originally Posted by Jman115

I understand that 36 sqft is a perfect square and that is the area these plants take up. But if each side was 6 ft long then you would have 4.89897 flowers per side. You cannot put PART of a flower in a space. That is why i said based on context this seems impossible.

Unless some flowers take up a rectangular area, while others are taking up squares. But that seems an odd thing to do. You would think each flowers area would need to be a specific shape.

And yeah I know 1.5 sqft means that I just had a dumb moment there.

No, that is not an odd thing to do at all. And you certainly don't plant every flower in exactly the same shape or even the same area.

Practically, arrange 5x5 flowers, with one missing. This will be (5*1.5)x(5*1.5) = 7.5x7.5 feet on a side.

Theoretically, you need 36 square feet. Maybe the plants are infinitely small but need the nutrients from 1.5 square feet. Who knows? That's 6x6.

Originally Posted by Deveno

i see no reason why 4 rows of flowers spaced 1.5 feet apart, with the flowers in each row spaced 1 foot apart (6 per row), would not satisfy the problem

(or 6 rows spaced 1 foot apart, with 4 flowers in each row spaced 1.5 feet apart, if you prefer). the space allotted to each flower is then 1.5 square feet.

My mind just had the flowers in square boxes, I assumed the flowers needed the same space to grow in each direction. But I guess the problem doesn't dictate that so that does work. My knowledge working with gardens is each plant DOES need to be in the same shape so yes it would be odd if you mixed them. But your solution ha them all in the same shape. I was just stuck on squares. Thank you.

Originally Posted by Jman115

My mind just had the flowers in square boxes, I assumed the flowers needed the same space to grow in each direction. But I guess the problem doesn't dictate that so that does work. My knowledge working with gardens is each plant DOES need to be in the same shape so yes it would be odd if you mixed them. But your solution ha them all in the same shape. I was just stuck on squares. Thank you.

24 1.5 sq ft floor tiles do not fit into a 36 sq ft room. You require a 6.1X 6.1 ft room which holds 25 tiles

Wilmer the Gardener says:

Row1: four 1 by 1.5 : lying on 1.5 length
Row2: six 1.5 by 1 : lying on 1 width
Row3: four 1 by 1.5 : on 1.5
Row4: six 1.5 by 1 : on 1
Row5: four 1 by 1.5 : on 1.5

Perfect fit of 24 in a 6 by 6

Originally Posted by Wilmer

Wilmer the Gardener says:

Row1: four 1 by 1.5 : lying on 1.5 length
Row2: six 1.5 by 1 : lying on 1 width
Row3: four 1 by 1.5 : on 1.5
Row4: six 1.5 by 1 : on 1
Row5: four 1 by 1.5 : on 1.5

Perfect fit of 24 in a 6 by 6

I left out one word in my reply " square " tiles

Thanks so much to all who helped clarify this for me. Can always count on you guys.

Code:

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|     |     |     |     | : 4 "1 by 1.5" lengthwise
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Hmmm....so simple we all missed it?