Let radius be 1 unit for each quarter circle ("quadrant").

Length of rectangle = 2 units + 17 cm
Breadth of rectangle = 2 units + 3 cm

Difference = 14 cm

Since length : breadth = 12 : 5 with a difference of 7,

7 ratio units (not the same as the radius units which I introduced earlier) --> 14
1 ratio unit --> 2
12 ratio units --> 24
5 ratio units --> 10

So the length of the rectangle is 24 cm and the breadth of the rectangle is 10 cm.

2 units + 3 cm --> 10 cm
2 units --> 7 cm
1 unit --> 3.5 cm

Perimeter of the shaded part
= 4 x curved part of the quadrants + 2 x 17 + 2 x 3
= (a full circumference of a circle with radius 3.5 cm) + 34 + 6
= 2 x 3.14 x 3.5 + 40
= 21.98 + 40
= 61.98 cm