# Gardens

The garden has a square shape with a circumference of 124 m. Divide it into two rectangular gardens; one should have a circumference of 10 meters more than the second. What size will the gardens be?

a =  31 m
b =  18 m
c =  31 m
d =  13 m

### Step-by-step explanation:

a = 124/4
c = a
2(a+b) = 10+2(c+d)
b+d = a

a = 124/4
c = a
2·(a+b) = 10+2·(c+d)
b+d = a

4a = 124
a-c = 0
2a+2b-2c-2d = 10
a-b-d = 0

Row 2 - 1/4 · Row 1 → Row 2
4a = 124
-c = -31
2a+2b-2c-2d = 10
a-b-d = 0

Row 3 - 2/4 · Row 1 → Row 3
4a = 124
-c = -31
2b-2c-2d = -52
a-b-d = 0

Row 4 - 1/4 · Row 1 → Row 4
4a = 124
-c = -31
2b-2c-2d = -52
-b-d = -31

Pivot: Row 2 ↔ Row 3
4a = 124
2b-2c-2d = -52
-c = -31
-b-d = -31

Row 4 - -1/2 · Row 2 → Row 4
4a = 124
2b-2c-2d = -52
-c = -31
-c-2d = -57

Row 4 - Row 3 → Row 4
4a = 124
2b-2c-2d = -52
-c = -31
-2d = -26

d = -26/-2 = 13
c = -31/-1 = 31
b = -52+2c+2d/2 = -52+2 · 31+2 · 13/2 = 18
a = 124/4 = 31

a = 31
b = 18
c = 31
d = 13

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