Discussion
Length of a rectangle is 12cm more than its breadth and it has a perimeter of 200cm. What will be diameter of a circle whose area matches the area of this rectangle?
Answer: B
Find the rectangle's sides from its perimeter first.
\[ 2\big((b + 12) + b\big) = 200 \quad\Longrightarrow\quad 2b + 12 = 100 \]
\[ b = 44 \text{ cm}, \qquad l = 56 \text{ cm} \]
\[ A = 56 \times 44 = 2464 \text{ cm}^{2} \]
Now set the circle's area equal to it, with \( \pi = \tfrac{22}{7} \):
\[ \frac{22}{7}r^{2} = 2464 \quad\Longrightarrow\quad r^{2} = \frac{2464 \times 7}{22} = 784 \]
\[ r = 28 \text{ cm} \quad\Longrightarrow\quad d = 56 \text{ cm} \]
The question asks for the diameter, so the radius of 28 cm must be doubled - and 28 is offered as a distractor for exactly that reason.
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