Question

A wire is bent in the form of rectangle having length twice the breadth. The same wire is bent in the form of circle. It was found that the area of the circle is greater than that of the rectangle by 104.5 sq. CM. Find the length of the wire

Answer 1

Answer: The length of wire would be 66 cm.

Step-by-step explanation:

Let breadth of the rectangular wire be x.

So,

Length= 2x

Perimeter of rectangular wire= 2(l+b)= 2(2x+x)= 6x

Circumference of circular  wire= Perimeter of rectangular wire

Circumference of circular wire= 2*pi*r

6x= 2*pi*r

r= 3x/pi

Area of rectangular wire= l*b= 2x*x= 2x^2

Area of circular wire= pi*r^2

Plugging the value of r in the above equation

Area of circular wire= pi*(3x/pi)^2= pi*9x^2/pi^2= 9x^2/pi

According to the question

Area of circular wire= Area of rectangular wire + 104.5

9x^2/pi= 2x^2 + 104.5

x^2(9/pi-2)= 104.5

x^2= 104.5*22/19= 5.5*22= 121

x^2= 121

Taking square root both side, we get

x= 11

So

Length of wire= 6x= 6*11= 66 cm