An engineer is measuring the width of an expanding crack in a wall. He fixes a thin piece of uniform wire, with its ends affixed to either side of the crack as shown in the diagram and measures its resistance \(R\). The crack widens and the wire's length increases by 40%. The wire's volume remains constant. In percentage, how much has \(R\) increased?
Assume that the wire remains uniform and ignore any 'leaks' of current to the wall or surroundings.