In the figure, GHIJKLMN is a cube of side a. Find the length of HN.
A.
\(\sqrt{3a}\)
B.
3a
C.
3a2
D.
a\(\sqrt{2}\)
E.
a\(\sqrt{3}\)
Correct answer is E
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