Discussion
The perimeter of a circle is equal to the perimeter of a rectangle whose length and breadth are respectively 14 centimetre and 8 centimetre. The area of the circle will be
Answer: A
The area of the circle is 154 square centimetre.
The rectangle's perimeter is \(2(14 + 8) = 44\) cm, which equals the circle's circumference:
\[ \begin{aligned} 2 \pi r &= 44 \\ r &= \frac{44 \times 7}{2 \times 22} = 7 \\ \pi r^{2} &= \frac{22}{7} \times 49 = 154 \end{aligned} \]
308 is twice the area, 77 is half of it, and 112 is the area of the rectangle (14 × 8), not of the circle.
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