I cannot for the life of me begin to figure out this problem. I have completed all others, but this one has just gotten me stumped!
Bryce, Dwayne, Julianna and Sonya share a 48m x 48m rectangular portion of the community garden in their neighbourhood. Within this space, each has an individual rectangular garden plot.
Bryce is the only one with a square plot. Its area is 1/2 the area of Dwayne's.
The area of Bryce's plot is 2/3 the area of Julianna's garden. Their plots have one side in common.
Sonya's garden has an area twice that of Julianna's garden.
What are the dimensions (length and width) of each person's garden plot?
Bryce, Dwayne, Julianna and Sonya share a 48m x 48m rectangular portion of the community garden in their neighbourhood. Within this space, each has an individual rectangular garden plot.
Bryce is the only one with a square plot. Its area is 1/2 the area of Dwayne's.
The area of Bryce's plot is 2/3 the area of Julianna's garden. Their plots have one side in common.
Sonya's garden has an area twice that of Julianna's garden.
What are the dimensions (length and width) of each person's garden plot?
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Total area of garden: 1920 square meters.
Bryce's plot is x
Julianna's garden is 3x/2 (x = 2y/3 if Julianna's plot is y. Work that out to y = 3x/2)
Sonya's garden is 3x
Dwayne's is 2x
So x + 3x/2 + 3x + 2x = 1920
2x + 3x + 6x + 4x = 3840
15x = 3840
x = 256.
So Bryce's plot is 256 square meters, and since it's square it must be 16 feet on a side.
Dwayne's is 512 square meters, but we don't know the dimensions.
Julianna's is 3x/2 of 256 so work that out to get 384 square feet
Sonya's is 768 square meters.
And we know that if Bryce's plot is 16 feet on each side, then Julianna's must be 16 X 24.
So from here you have to draw it out, I think. Put Dwayne's in one corner and Julianna's next to it so you get 40 feet in length when you combine the two.
Bryce's plot is x
Julianna's garden is 3x/2 (x = 2y/3 if Julianna's plot is y. Work that out to y = 3x/2)
Sonya's garden is 3x
Dwayne's is 2x
So x + 3x/2 + 3x + 2x = 1920
2x + 3x + 6x + 4x = 3840
15x = 3840
x = 256.
So Bryce's plot is 256 square meters, and since it's square it must be 16 feet on a side.
Dwayne's is 512 square meters, but we don't know the dimensions.
Julianna's is 3x/2 of 256 so work that out to get 384 square feet
Sonya's is 768 square meters.
And we know that if Bryce's plot is 16 feet on each side, then Julianna's must be 16 X 24.
So from here you have to draw it out, I think. Put Dwayne's in one corner and Julianna's next to it so you get 40 feet in length when you combine the two.
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Start with bryce. Draw a square. Label it as x by x
Go Right. Draw a rectangle that is x by 2x. Make sure the x side is the width of Dwayne's plot. His length is 2x.
Go down from Bryce's plot. Draw a line for the length of Julianne's plot. Her length is 1.5x. That will make Bryce's plot 2/3 of hers. Proof: Here area = x*y and y = 1.5x. That means that her area = 1.5x^2. Therefore his area is 1/1.5 of hers which is 2/3 x^2
Go Right. Draw a rectangle that is x by 2x. Make sure the x side is the width of Dwayne's plot. His length is 2x.
Go down from Bryce's plot. Draw a line for the length of Julianne's plot. Her length is 1.5x. That will make Bryce's plot 2/3 of hers. Proof: Here area = x*y and y = 1.5x. That means that her area = 1.5x^2. Therefore his area is 1/1.5 of hers which is 2/3 x^2
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