Let the initial length of the copper rod be $L_{\text{Cu}}$ and that of the aluminium rod be $L_{\text{Al}}$. The increase in length of the copper rod for a temperature rise of $\Delta T$ is given by: $\Delta L_{\text{Cu}} = L_{\text{Cu}} \alpha_{\text{Cu}} \Delta T$ The increase in length of the aluminium rod for the same temperature rise is: $\Delta L_{\text{Al}} = L_{\text{Al}} \alpha_{\text{Al}} \Delta T$ It is given that the increase in their lengths is equal, irrespective of the increase in temperature. Therefore: $\Delta L_{\text{Cu}} = \Delta L_{\text{Al}}$ $L_{\text{Cu}} \alpha_{\text{Cu}} \Delta T = L_{\text{Al}} \alpha_{\text{Al}} \Delta T$ $L_{\text{Cu}} \alpha_{\text{Cu}} = L_{\text{Al}} \alpha_{\text{Al}}$ Substituting the given values ($L_{\text{Cu}} = 88 \text{ cm}$, $\alpha_{\text{Cu}} = 1.7 \times 10^{-5} \text{ K}^{-1}$, $\alpha_{\text{Al}} = 2.2 \times 10^{-5} \text{ K}^{-1}$): $88 \times 1.7 \times 10^{-5} = L_{\text{Al}} \times 2.2 \times 10^{-5}$ $L_{\text{Al}} = \frac{88 \times 1.7}{2.2} = \frac{88 \times 17}{22} = 4 \times 17 = 68 \text{ cm}$.