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?
(1) 24 cm
(2) 26 cm
(3) 52 cm
(4) Cannot be determined
(5) None of these

Answer 1

Let l be length and b be breadth if rectangle.
Let d be diameter and r be radius of circle.
l = 2d
=2(2r)
=4r

Circumference= Area of a square of side 22 cm
That is:
2*pi*r = 22*22
r= (22*22)/(2*pi)
r= 77.07 cm

Therefore:
l= 4r
= 4* 77.07
=308.28 cm

Given: perimeter = 668

2(l + b) = 668
2(308.28+b) = 668
308.28 + b = 334
b = 334 - 308.28
=25.7
= 26 (approx.)

Answer is (2) 26 cm