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30 Jun 2022, 23:30
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:42) correct
32%
(01:57)
wrong
based on 28
sessions
History
Date
Time
Result
Not Attempted Yet
If the space diagonal of cube C is 5 inches long, what is the length, in inches, of the diagonal of the base of cube C?
A. 5/(√6)
B. 5·√(2/3)
C. 5·√(3/2)
D. 5·√3
E. 5·√6
A. 5/(√6)
B. 5·√(2/3)
C. 5·√(3/2)
D. 5·√3
E. 5·√6
02 Jul 2022, 06:22
Kudos
Bookmarks
Bunuel
Breaking Down the Info:
Let us assume we have a cube with a side length of 1. We can slice the cube across two diagonal edges to get two triangular prisms. The face we created with the slice is a 1 by \(\sqrt{2}\) rectangle. Thus the diagonal of this rectangle, which is also the diagonal of cube C, is \(\sqrt{3}\) from Pythagorean's theorem.
Finally, we know the diagonal of the base to the diagonal of the cube is \(\sqrt{2}:\sqrt{3} = x:5\). Then \(x = 5*\sqrt{\frac{2}{3}}\)
Answer: B
