Square into three rectangles

Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.

Correct result:

a =  12
b =  3
c =  9
d =  6
o1 =  30
o2 =  30
o3 =  30
o4 =  32

Solution:

a=12
o1 = 2(a+b)
o2 = 2(c+d)
o3 = 2(c+d)
o1=o2
b+c=a
2d = 12
o4 = 2(a+a/3)

a=12
o1 = 2•(a+b)
o2 = 2•(c+d)
o3 = 2•(c+d)
o1=o2
b+c=a
2•d = 12
o4 = 2•(a+a/3)

a = 12
2a+2b-o1 = 0
2c+2d-o2 = 0
2c+2d-o3 = 0
o1-o2 = 0
a-b-c = 0
2d = 12
8a-3o4 = 0

a = 12
b = 3
c = 9
d = 6
o1 = 30
o2 = 30
o3 = 30
o4 = 32

Our linear equations calculator calculates it.

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Showing 1 comment:
Dr Math
so the solution is

1. 12*3 ...  a = 12 * b = 3
2. 9*6 ... c = 9 * d = 6
3. 9*6 ... c = 9 * d = 6

o1 is the circumference of the first, o2 the second, o3 the third rectangle
o4 is a circumference if the square is divided into same   12 * 4 rectangles

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