# Circumference 8142

Divide a rectangle with sides 60 mm and 84 mm long into three rectangles with the same circumference.

a =  51
b =  42
c =  9
d =  84

## Step-by-step explanation:

a+c=60
b+b = 84
d = 84
2(a+b) = 2(c+d)

a+c=60
b+b = 84
d = 84
2·(a+b) = 2·(c+d)

a+c = 60
2b = 84
d = 84
2a+2b-2c-2d = 0

Pivot: Row 1 ↔ Row 4
2a+2b-2c-2d = 0
2b = 84
d = 84
a+c = 60

Row 4 - 1/2 · Row 1 → Row 4
2a+2b-2c-2d = 0
2b = 84
d = 84
-b+2c+d = 60

Row 4 - -1/2 · Row 2 → Row 4
2a+2b-2c-2d = 0
2b = 84
d = 84
2c+d = 102

Pivot: Row 3 ↔ Row 4
2a+2b-2c-2d = 0
2b = 84
2c+d = 102
d = 84

d = 84/1 = 84
c = 102-d/2 = 102-84/2 = 9
b = 84/2 = 42
a = 0-2b+2c+2d/2 = 0-2 · 42+2 · 9+2 · 84/2 = 51

a = 51
b = 42
c = 9
d = 84

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