In a

In a triangle, the aspect ratio a: c is 3:2, and a: b is 5:4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides.

Correct answer:

a =  30
b =  24
c =  20

Step-by-step explanation:


a+b+c=74
a= 3/2·c
a = b· 5/4

a+b+c = 74
2a-3c = 0
4a-5b = 0

Pivot: Row 1 ↔ Row 3
4a-5b = 0
2a-3c = 0
a+b+c = 74

Row 2 - 2/4 · Row 1 → Row 2
4a-5b = 0
2.5b-3c = 0
a+b+c = 74

Row 3 - 1/4 · Row 1 → Row 3
4a-5b = 0
2.5b-3c = 0
2.25b+c = 74

Row 3 - 2.25/2.5 · Row 2 → Row 3
4a-5b = 0
2.5b-3c = 0
3.7c = 74


c = 74/3.7 = 20
b = 0+3c/2.5 = 0+3 · 20/2.5 = 24
a = 0+5b/4 = 0+5 · 24/4 = 30

a = 30
b = 24
c = 20

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