A circular wire of length 168 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 5 : 7. What is the length (in cm) of the diagonal of the rectangle?

Let, length of the rectangle = 5x and breadth =  7x

A circular wire of length 168 cm is cut and bent in the form of rectangle i.e perimeter of the rectangle.

$$\therefore$$ 2(5x + 7x) = 168 $$\Rightarrow$$ 24x = 168 $$\Rightarrow$$ x = 7

Length = 35cm and Breadth = 49cm

Now, diagonal of the rectangle = $$\sqrt{35^{2} + 49^{2}}$$

 $$\Rightarrow\sqrt{1225 + 2401}\Rightarrow\sqrt{3626}$$

Hence, option D is the correct answer.