Answer:
Let \[x\] be the length of each rod. The rates of flow of heat through the rods A and B will be equal if \[\frac{{{K}_{1}}{{A}_{1}}({{T}_{1}}-{{T}_{2}})}{x}=\frac{{{K}_{2}}{{A}_{2}}({{T}_{1}}-{{T}_{2}})}{x}\] or \[{{K}_{1}}{{A}_{1}}={{K}_{2}}{{A}_{2}}\] or \[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{{{K}_{2}}}{{{K}_{1}}}\] Hence for equal rates of flow of heat, the areas of cross-section of the two rods should be inversely proportional to their coefficients of thermal conductivity.
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