Given:

The ratio of lengths:
The ratio of diameters:
Both wires are subject to the same stretching force, and since they are made of the same material, their Young's modulus is the same.

The elongation ( ) of a wire subject to a force is given by:
where is the force applied, is the original length, is the cross-sectional area, and is Young's modulus.

For wires and :

Since and , the ratio of their elongations becomes:

The cross-sectional area is a function of diameter, . Therefore,

Substituting these into the elongation ratio:

Substitute the given ratios:

Thus, the ratio of the elongations of wires and is .