Question

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?

• A. $24cm$
• B. $26cm$
• C. $52cm$
• D. Cannot be determined

Answer 1

The correct option is B $26cm$

Given that, circumference of the circle is equal to the area of a square of side $22cm$.

We know that, circumference of a circle is $2\pi r$

and area of a square is $side\times side$

$\therefore 2\pi r=side\times side$
$\Rightarrow 2\times \frac{22}{7}\times radius=22\times 22[\because \pi =\frac{22}{7}]$
$\Rightarrow$ radius $\left(r\right)=77cm$
Given that, the length of a rectangle is twice the diameter of a circle.
$\Rightarrow$ length $=2(77\times 2)=308cm[\because d=2r]$
Also given that, the perimeter of the rectangle is $668cm$.

$\therefore 2(length+breadth)=668$
$\Rightarrow length+breadth=334cm$
$\Rightarrow 308+breadth=334[\because length=308cm]$
$\Rightarrow$ breadth $=26cm$

Hence, the breadth of the rectangle is $26cm$.