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 =  0.4167
r = (Correct answer is: 3:4:5)

Solution:

$C=1-{\displaystyle \frac{1}{4}}-{\displaystyle \frac{1}{3}}={\displaystyle \frac{5}{12}}=0.4167$

$$\begin{gathered} r={\displaystyle \frac{1}{4}}:{\displaystyle \frac{1}{3}}:{\displaystyle \frac{5}{12}} \\ r={\displaystyle \frac{3}{12}}:{\displaystyle \frac{4}{12}}:{\displaystyle \frac{5}{12}} \\ r=3:4:5 \end{gathered}$$

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