In the figure, GHIJKLMN is a cube of side a. Find the length of HN.
Attached Figure / Diagram
A
\(\sqrt{3a}\)
B
3a
C
3a2
D
a\(\sqrt{2}\)
E
a\(\sqrt{3}\)
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
HJ2 = a2 + a2 = 2a2
HJ = \(\sqrt{2a^2} = a \sqrt{2}\)
HN2 = a2 + (a\(\sqrt{2}\))2 = a2 + 2a2 = 3a2
HN = \(\sqrt{3a^2}\)
= a\(\sqrt{3}\)cm
Source: Myschool Past Questions Archive (Record #32814)