Practice | Hashtable

1. If the total length of diagonals of a cube is 12 cm, then what is the total length of the edges of the cube ?

A. 6 $\sqrt{3}$ cm

B. 12 cm

C. 15 cm

D. 12 $\sqrt{3}$ cm

Solution:

Since a cube has 4 diagonals, we have :
Length of a diagonal

\begin{aligned} = (\frac{12}{4}) c m \\ = 3 c m \end{aligned}

Let the length of each edge of the cube be a cm
Then,

\begin{aligned} \sqrt{3} a = 3 \\ o r, a = \sqrt{3} \end{aligned}

∴ Total length of the edges of the cube =

12 \sqrt{3}

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