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Q.

The length of a rectangle is twice the diameter of a circle. The circumference of the circle is equal to the area of a square of side 22 cm. What is the breadth of the rectangle, if its perimeter is 668 cm?


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a

24 cm

b

26 cm

c

52 cm

d

Non-existent 

answer is B.

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Detailed Solution

We have been given,
The length of a rectangle is twice the diameter of a circle.
The circumference of the circle is equal to the area of a square of side 22 cm.
Equating both the formula,
2πr=side×side ⇒2×227×radius = 22×22 ⇒ Radius r=77 cm As we know the length of a rectangle is twice the diameter of a circle.
Thus, length = 2(2×radius).
⇒ Length =277×2
⇒ Length = 308 cm
We know, the perimeter of the rectangle is 668 cm.
∴ 2length+breadth=668 Solving further,
⇒length+breadth=334 cm ⇒308+breadth=334∵length=308 cm ⇒breadth =26 cm Therefore, the breadth of the rectangle is 26 cm.
Hence, option 2 is correct.
 
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