Okay so this question is a frame problem meant to be solved by turning the problem into a quadratic equation.
I'm having trouble extracting enough information from the problem. Or maybe I just don't know how to use the given information.
Here's the word problem:
A landscape architect is designing a rectangular flowerbed with 28 plants that are placed 1 meter apart.
He needs an inner rectangular space in the center for plants that must be 1 meter from the border of the bed
and that require 24 square meters for planting. What should the overall dimensions of the flowerbed be?
Ok, so here's what I think i've gathered from this problem.
All plants are placed 1 meter apart, but there are 2 different kinds of plants.
One kind forms the inner rectangle that has an area of 24 square meters, and they
must be 1 meter from the border, making the border width (frame width) 1.
The rest of the plants surround the inner rectangle forming a larger rectangle - total
area 28 square meters.
So, all I can confirm is that:
x=1 ;frame width
lw = 24 ;area of inner rectangle
(l+2x)(w+2x)=28 ;entire area, x = 1
I don't know how to turn this info into a quadratic that will give me the dimensions of the flowerbed.
The dimensions being: 6m x 8m
Obviously 6 x 8 = 48, meaning that the entire area must be 48 square meters, not 28.
And it maks sense, because (6-2(1))(8-2(1)) = 4 x 6 = 24. It works.
Possibly a typo, maybe it was supposed to be 48 total flowers instead of 28. If that's the case, I could have solved it
just by looking at it and thinking about the factors of 24.
But it's still possible that i'm completely misinterpreting the question.
Thanks.
I'm having trouble extracting enough information from the problem. Or maybe I just don't know how to use the given information.
Here's the word problem:
A landscape architect is designing a rectangular flowerbed with 28 plants that are placed 1 meter apart.
He needs an inner rectangular space in the center for plants that must be 1 meter from the border of the bed
and that require 24 square meters for planting. What should the overall dimensions of the flowerbed be?
Ok, so here's what I think i've gathered from this problem.
All plants are placed 1 meter apart, but there are 2 different kinds of plants.
One kind forms the inner rectangle that has an area of 24 square meters, and they
must be 1 meter from the border, making the border width (frame width) 1.
The rest of the plants surround the inner rectangle forming a larger rectangle - total
area 28 square meters.
So, all I can confirm is that:
x=1 ;frame width
lw = 24 ;area of inner rectangle
(l+2x)(w+2x)=28 ;entire area, x = 1
I don't know how to turn this info into a quadratic that will give me the dimensions of the flowerbed.
The dimensions being: 6m x 8m
Obviously 6 x 8 = 48, meaning that the entire area must be 48 square meters, not 28.
And it maks sense, because (6-2(1))(8-2(1)) = 4 x 6 = 24. It works.
Possibly a typo, maybe it was supposed to be 48 total flowers instead of 28. If that's the case, I could have solved it
just by looking at it and thinking about the factors of 24.
But it's still possible that i'm completely misinterpreting the question.
Thanks.
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