The area of rectangle is equal to area of circle with circumference equal to 39.6 m.What is the length of the rectangle if its breadth is 4.5 m.

The correct answer is: length = 27.72 m.

Step-by-step solution:-
For the given circle-
Circumference of a circle = 2πr
∴                           39.6 m = 2πr …................................................................. (From given information)
∴                            39.6 m = 2 × 22 / 7 × r .................................................................. (π = 22 / 7)
∴                            39.6 m = 44 / 7 × r
∴ 39.6 × 7 / 44 = r ....................................................................................... (Dividing both sides by 44/7)
∴ 6.3 = r ........................................................................... (Equation i)
Area of the given circle = πr2
∴ Area of the given circle = 22 / 7r2 .................................................................. (π = 22 / 7)
∴ Area of the given circle = 22 / 7 × (6.3)² ........................................................ (From Equation i)
∴ Area of the given circle = 22 / 7 × 39.69
∴ Area of the given circle = 124.74 m² ............................................................ (Equation ii)
From given information-
Area of circle = Area of rectangle .................................................................. (Equation iii)
∴       124.74 = Area of rectangle .................................................................. (Equation ii)
∴       124.74 = length × breadth ................................................................... (Area of a rectangle = length × breadth)
∴       124.74 = length × 4.5 ......................................................................... (From given information)
∴       124.74 / 4.5 = length
∴        length = 27.72 m.