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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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24 cm

26 cm

52 cm

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,

2 πr = side \times side

\Rightarrow 2 \times \frac{22}{7} \times radius

22 \times 22

\Rightarrow

Radius

(r) = 77 cm

As we know the length of a rectangle is twice the diameter of a circle.
Thus, length = 2(2

\times

radius).

\Rightarrow

Length

= 2 (77 \times 2)

\Rightarrow

Length = 308 cm
We know, the perimeter of the rectangle is

668 cm

∴ 2 (length + bread t h) = 668

Solving further,

\Rightarrow length + breadth = 334 cm

\Rightarrow 308 + breadth = 334 [∵ length = 308 cm]

\Rightarrow

breadth

= 26 cm

Therefore, the breadth of the rectangle is

26 cm

.
Hence, option 2 is correct.

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