Question : The perimeter of a minor sector of a circle of radius 5 cm is 15.5 cm. Find the area of the minor sector (use $\pi=\frac{22}{7}$ ).
Option 1: 17.53 cm2
Option 2: 13.75 cm2
Option 3: 13.57 cm2
Option 4: 17.35 cm2
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Correct Answer: 13.75 cm 2
Solution : Let AOB be the sector with O as the centre. Given: Radius = r = 5 cm Perimeter of sector = 15.5 cm So, OA + AB + OB = 15.5 ⇒ 5 + 5 + AB = 15.5 ⇒ AB = 5.5 cm = $l$ Area of sector = $\frac{1}{2}\times r \times l$ $=\frac{1}{2}\times 5 \times 5.5$ $=13.75$ cm 2 Hence, the correct answer is 13.75 cm 2 .
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