Three sides

Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, and c.

Correct answer:

a =  8
b =  17
c =  15

Step-by-step explanation:


b = 2+c
a = b-9
a+b+c = 40

b-c = 2
a-b = -9
a+b+c = 40

Pivot: Row 1 ↔ Row 2
a-b = -9
b-c = 2
a+b+c = 40

Row 3 - Row 1 → Row 3
a-b = -9
b-c = 2
2b+c = 49

Pivot: Row 2 ↔ Row 3
a-b = -9
2b+c = 49
b-c = 2

Row 3 - 1/2 · Row 2 → Row 3
a-b = -9
2b+c = 49
-1.5c = -22.5


c = -22.5/-1.5 = 15
b = 49-c/2 = 49-15/2 = 17
a = -9+b = -9+17 = 8

a = 8
b = 17
c = 15

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