A rectangular box has dimensions 6 by 8 by 10. Which value is closest to the length of its longest interior diagonal?

The space diagonal of a box is $\sqrt{l^2+w^2+h^2}=\sqrt{6^2+8^2+10^2}=\sqrt{36+64+100}=\sqrt{200}\approx14.1$, choice G. This comes from using the Pythagorean theorem twice: the base diagonal is $\sqrt{36+64}=10$, and then $\sqrt{10^2+10^2}=\sqrt{200}$. Choice F ($10$) is only the diagonal of the $6$ by $8$ face and leaves out the height. Choice J ($24$) adds the three dimensions, which would be a path along the edges, not a straight diagonal. Choice H ($18$) is not obtained from any of the correct steps. The diagonal must be shorter than the sum of the dimensions.