Discussion

Explanation:

Side of the cube $6\sqrt[3]{4}$ 
Volume of the cube = ${\left(6\sqrt[3]{4}\right)}^3$ = 864

Volume of the cuboid = 12 × 9 × height = 864

⇒ height = 8

Longest diagonal of the cuboid is the body diagonal

∴ Longest diagonal = $\sqrt{{12}^2+9^2+8^2}$ = 17

Hence, option (d).

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