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As a wire gets longer its resistance increases, and as it gets thinner its resistance also increases because its cross sectional area decreases. Doubling the length will double the resistance, but the wire also must get thinner as it is stretched, because it will contain the same amount of metal in twice the length.
Resistivity(denoted by rho) is electrical resistance per unit length and per unit of cross-sectional area. So new resistivity will also get doubled i.e. ... So the new resistance becomes 9 times the original resistance. The resistivity of the wire remains unchanged, as it only depends on the material of the wire.
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