Since it is divide into 3 sectors
then \(8x° = 360°\)
\(x° = 45°\)
The 3rd sector = 3 times the size of the other two sectors put together
= \(3(45 + 45) = 3(90) = 270°\)
Perimeter of a sector = \(2r + l\)
where r = radius of the circle ; l = length of arc = \(\frac{\theta}{360°} \times 2\pi r\)
Area of circle = \(\frac{22}{7} \times r^{2} = 154 cm^{2}\)
\(r^{2} = \frac{154 \times 7}{22} = 49\)
\(r = 7 cm\)
\(l = \frac{270}{360} \times 2 \times \frac{22}{7} \times 7 = 33 cm\)
Perimeter of sector = \(2(7) + 33 = 14 + 33 = 47 cm\).