Question

if the length of diagonal of a cube is 4 root 3 cm, then the length of its edge is

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Answer 1

Answer:

4 cm.

Step-by-step explanation:

$length \: of \: diagonal = 4 \sqrt{3} \\ formula \: of \: length \: of \: diagonal \: of \: a \: cube \: of \: side \: a \: cm \: = a \sqrt{3} \\ therefore \: \: \: \: a \sqrt{3} = 4 \sqrt{3} \\ = > a = 4 \: cm \\ edge \: of \: cube = 4 \: cm$

Answer 2

Answer:

4 cm.

Step-by-step explanation:

the length of the diagonal of a cube =√( a² + a² + a²) = √(3a²)

So , √(3a²) = 4√3

{√(3a²)}² = {4√3 }² [ squaring both sides of the equation]

3a² = 16 * 3

a² = 48/3

a² = 16

a = √16

a= ± 4

but edge length cannot be negative , so edge = 4 cm