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What is the greatest distance (in inches) between any two corners of a rectangular box with dimensions of 6 inches, 8 in

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by Vincen » Thu Jul 30, 2020 8:07 am

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What is the greatest distance (in inches) between any two corners of a rectangular box with dimensions of 6 inches, 8 inches, and 10 inches?

A. 10 inches
B. 12 inches
C. \(10\sqrt2\) inches
D. \(10\sqrt3\) inches
E. 24 inches

[spoiler]OA=C[/spoiler]

Source: Princeton Review
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Re: What is the greatest distance (in inches) between any two corners of a rectangular box with dimensions of 6 inches,

by Scott@TargetTestPrep » Wed Aug 05, 2020 10:19 am
Vincen wrote: ↑
Thu Jul 30, 2020 8:07 am
 What is the greatest distance (in inches) between any two corners of a rectangular box with dimensions of 6 inches, 8 inches, and 10 inches?

A. 10 inches
B. 12 inches
C. \(10\sqrt2\) inches
D. \(10\sqrt3\) inches
E. 24 inches

[spoiler]OA=C[/spoiler]

Solution:


Recall that if a rectangular box has dimensions x, y, and z, then the longest segment that can fit into the box (and thus containing two corners of the box) is called the space diagonal and has a length of:

√(x^2 + y^2 + z^2)

Therefore, here the greatest distance between any two corners of the rectangular box is:

√(6^2 + 8^2 + 10^2) = √200 = 10√2 inches

Answer: C

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