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EEJ MAIN Aptitude QUESTION #10988
Question 1
A cuboid has dimensions $6 \times 4 \times 3$ units. What is the area of the largest triangular cross-section that can be obtained by cutting the cuboid with a plane passing through exactly three of its vertices?
  • $3\sqrt{29}$✔️
  • $6\sqrt{14}$
  • $12\sqrt{5}$
  • $18\sqrt{2}$
Correct Answer Explanation
The maximum area triangle uses three vertices not all on the same face, e.g., $(0,0,0)$, $(6,4,0)$, and $(6,0,3)$. Vectors: $\vec{u} = (6,4,0)$ and $\vec{v} = (6,0,3)$. Cross product: $\vec{u} \times \vec{v} = (12, -18, -24)$ with magnitude $\sqrt{144 + 324 + 576} = \sqrt{1044} = 6\sqrt{29}$. Area = $\frac{1}{2} \times 6\sqrt{29} = 3\sqrt{29}$.