A rectangular solid has dimensions $3 \times 4 \times 6$. What is its **diagonal** (the longest straight line that fits inside)?
A$\sqrt{13}$
B$\sqrt{61}$
C$13$
D$\sqrt{52}$
Answer & Solution
Correct answer: B. $\sqrt{61}$
The space diagonal of a rectangular solid with dimensions $\ell \times w \times h$ is $\sqrt{\ell^{2} + w^{2} + h^{2}}$.
$\sqrt{3^{2} + 4^{2} + 6^{2}} = \sqrt{9 + 16 + 36} = \sqrt{61}$.
- Trap D ($13 = 3 + 4 + 6$) adds dimensions.
- Trap A and B come from miscombining squares.
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