[Guest]

Bryce, Duane, Julianna, and Sonya share a 40 feet by 48 feet rectangular portion of the community garden in their neighborhood. Within this space, each has their own rectangular garden plot.

Bryce is the only one with a square plot. Its area is 1/2 the area of Duane’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.

[Guest]

I'll assume the question is "what are the dimensions of each plot?"

Let:

BW = width of Bryce's plot

BL = length of Bryce's plot

DW = width of Duane's plot

DL = length of Duane's plot

JW = width of Julianna's plot

JL = length of Julianna's plot

SW = width of Sonya's plot

SL = length of Sonya's plot

From clue #1:

BW*BL = DW*DL/2

BW = BL

From clue #2:

BW*BL = JW*JL*2/3

BW = JW

Furthermore, since B and J's plots must share a side, S and D's must as well. Draw the rectangles to see why.

SW = DW

From clue #3 we

SW*SL = JW*JL*2

Also, since we know adjacent plots from clue #2, we can relate the length of plots to the length of the garden.

either:

BL+JL = 40

SL+DL = 48

or

BL+JL = 48

SL+DL = 40

Alternatively, you could do:

BW+BL+DW+DL+SW+SL+JW+JL=176 (perimeter of garden)

BW*BL+DW*DL+JW*JL+SW*SL=1920 (area of garden)

So you don't have to guess which set of 40,48 is correct. I think those equations are more cumbersome to work with though.

Either way, it's eight equations and eight variables. Solving yields:

BW = 16

BL = 16

JW = 16

JL = 24

SW = 32

SL = 24

DW = 32

DL = 16

[Guest]

Community garden:

[Guest]

Used matrices to find the relationship of each plot to each other, added them together with the least term, set it equal to 40x48, solved for the area of each platt, from there I too the square root of Bryce's area to find the sides, then it was easy from there. I got the same answer as posted above.

The puzzle should probably distinguish that by "Their plots have one side in common." they mean the common side is the same length for each of them, it is possible it could have meant that they are merely next to each other and not necessarily that it is 16 for each.

[bonanova]

Plot sizes: 2B / 3J / 4D / 6S = 256B / 384J / 512D / 768S

B is square and J has side in common

B=16x16 J=16x24

Split 32x40 according to 4D 6S

D=16X32 S=24x32 or

D=12.8x40 S=19.4x40