# Circumference 3088

In the parallelogram ABCD, the side AB is three times longer than the side BC. The circumference of the parallelogram is 20 cm. Find the lengths of the sides of the parallelogram.

a =  7.5
b =  2.5
c =  7.5
d =  2.5

### Step-by-step explanation:

2(a+b)=20
a=3b
c=a
d=b

2·(a+b)=20
a=3·b
c=a
d=b

2a+2b = 20
a-3b = 0
a-c = 0
b-d = 0

Row 2 - 1/2 · Row 1 → Row 2
2a+2b = 20
-4b = -10
a-c = 0
b-d = 0

Row 3 - 1/2 · Row 1 → Row 3
2a+2b = 20
-4b = -10
-b-c = -10
b-d = 0

Row 3 - -1/-4 · Row 2 → Row 3
2a+2b = 20
-4b = -10
-c = -7.5
b-d = 0

Row 4 - 1/-4 · Row 2 → Row 4
2a+2b = 20
-4b = -10
-c = -7.5
-d = -2.5

d = -2.5/-1 = 2.5
c = -7.5/-1 = 7.5
b = -10/-4 = 2.5
a = 20-2b/2 = 20-2 · 2.5/2 = 7.5

a = 15/2 = 7.5
b = 5/2 = 2.5
c = 15/2 = 7.5
d = 5/2 = 2.5

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