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The correct answer for determining the recommended length of a rivet when joining materials of different thicknesses, such as a .032-inch and a .064-inch aluminum alloy, is based on the total thickness of the materials and the necessary grip length required for the rivet to create a secure joint.

In this case, the combined thickness of the materials being joined is .032 inches plus .064 inches, which equals .096 inches. To ensure adequate grip for the rivet while also allowing for the required installation process (which involves the rivet expanding and potentially becoming deformed), it is recommended to lengthen the rivet beyond just the combined thickness of the materials.

The suggested formula, which involves taking one and one-half times the rivet diameter plus an additional .096 inch to accommodate the materials being joined, helps in achieving proper engagement of the rivet in both pieces being fastened. This allows for the necessary mechanical strength and integrity of the joint during use.

Thus, selecting one and one-half times the rivet diameter plus .096 inch provides the additional length needed beyond the merely combined thickness of the materials, ensuring a reliable and effective fastening method.