A rectangular paper is folded along its diagonal to form a polygon as shown in the following figure. If the ratio of the area of this polygon to that of the rectangle is $\frac{16}{5}$, the ratio of the length to the breadth of the original rectangle is:

  

Three equal circles each of radius $1 \mathrm{cm}$ are circumscribed by a larger circle. Find the perimeter of the circumscribing circle.

Three circular rings of equal radii of $1 \mathrm{cm}$ each are touching each other. A string runs all around the set of rings very tightly. What is the minimum length of string required to bind all the three rings in the given manner?

An equilateral triangle circumscribes all the three circles each of radius $1\mathrm{cm}$. What is the perimeter of the equilateral triangle?

Six circles each of unit radius are being circumscribed by another larger circle. All the smaller circles touch each other. What is the circumference of the larger circle?

There are six circular rings of iron, kept close to each other. A string binds them as tightly as possible. If the radius of each circular iron ring is $1 \mathrm{cm}$. What is the minimum possible length of string required to bind them?

An equilateral triangle circumscribes all the six circles, each with radius $1 \mathrm{cm}$. What is the perimeter of the equilateral perimeter of the equilateral triangle?