Aptitude Hack#61(25-4-19)

Question:
 The area of a square is 196 sq cm whose side is half of the radius of a circle. The circumference of the circle is equal to the breadth of a rectangle if the perimeter of a rectangle is 712 cm. What is the length of the rectangle?  

A) 196 cm

B) 186 cm

C) 180 cm

D) 190 cm 

E)  None of these


Answer: C)180 cm

Explanation:

Given, Area of a square = 196 sq cm
W.K.T: Area of square = (side)^2
=> (side)^2 = 196
=> side = sqrt(196)
=> side of square = 14 cm

Given, side of square = (1/2) of radius of circle
=> 14 = r/2
=> r = 14 * 2
=> r = 28 cm

Circumference of circle = 2 * pi * r
= 2 * (22/7) * 28
= 2 * 22 * 4
= 176

Given, Circumference of circle = breadth of rectangle
=> b = 176 cm

Given, Perimeter of rectangle = 712
=> 2(l + b) = 712
=> 2(l + 176) = 712
=> (l + 176) = 712 / 2
=> l + 176 = 356
=> l = 356 - 176
=> l = 180 cm

Thus, the length of the rectangle = 180 cm.