JAMB - Mathematics (1985 - No. 44)

In the figure, GHIJKLMN is a cube of side a. Find the length of HN.
\(\sqrt{3a}\)
3a
3a2
a\(\sqrt{2}\)
a\(\sqrt{3}\)

Explanation

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

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