The small rectangle consists of 12 of the radii of the circles, each connecting a point of contact to the centre of the relevant circle. These are shown in green and orange in the diagram on the right.
Since this has a total length of 60\text{cm}, each radius is of length 60\text{cm} \div 12 = 5\text{cm}.
The large rectangle can also be broken down into segments of this length. These are shown in blue and red on the diagram. There are 20 of these, so the perimeter of the large rectangle is 5\text{cm} \times 20 = 100\text{cm} = 1\text{m}.