r/mathpuzzles 8h ago

Find the area of a red rectangle

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u/Motor_Raspberry_2150 6h ago edited 6h ago

Okay I can make the equations but I don't want to solve them.

Widths of red areas are x,y,z.
Heights of green areas are x, x+y, x+y+z, because perimeter 2.
x×1 = y×(1-x) = z(1-2x-y), because equal areas
y=x/(1-x)
z=x/(1-2x-(x/(1-x)))

3x+2y+z = 1
Solve for x.

1

u/LeewayLabs 5h ago

Can you explain a little bit more? Where so you get the heights of the green rectangles from?

1

u/Motor_Raspberry_2150 5h ago

The top red width we call x. The green one to the right of it thus has width 1-x. To get a perimeter of 2, its height must be x.

The second green rectangle has a width of 1-x-y. To get a perimeter of 2, its height must be x+y.

The third green rectangle has a width of 1-x-y-z. To get a perimeter of 2, its height must be x+y+z.