Three segments

The circle is divided into 3 segments. Segment A occupies 1/4 of the area, segment B occupies 1/3 of the area. What part is occupied by section C? In what proportion are areas A: B: C?

Result

C =  0.417
r = (Correct answer is: 3/4:5) Wrong answer

Solution:

C=1−14−13=512≐0.4167≐0.417C=1 - \dfrac{ 1 }{ 4 } -\dfrac{ 1 }{ 3 }=\dfrac{ 5 }{ 12 } \doteq 0.4167 \doteq 0.417
r=14:13:512 r=312:412:512  r=3:4:5r=\dfrac{ 1 }{ 4 } :\dfrac{ 1 }{ 3 } :\dfrac{ 5 }{ 12 } \ \\ r=\dfrac{ 3 }{ 12 } :\dfrac{ 4 }{ 12 } :\dfrac{ 5 }{ 12 } \ \\ \ \\ r=3:4:5

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