Question

The diagonal of cube is root 12cm. What is length of its edge??

Answer 1

Hello...

length of diagonal = √12 cm

length of diagonal = √3 × Length of edge 

√12 = √3 × Length of edge of the cube

Length of edge of the cube = √12 / √3

  = 2√3 / √3 = 2

Answer 2

The length of its edge is  2 cm.

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Let's understand a few concepts:

To find the length of the edge we will use the following formula of diagonal of a cube:

$\bigstar\:\boxed{\bold{Diagonal \:of\:a\:cube = \sqrt{3} \times edge }}\:\bigstar$

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Let's solve the given problem:

The diagonal of a cube = $\sqrt{12} \:cm$

Let "a" cm be the edge of the given cube.

By using the above formula of the diagonal of a cube, we can form the following equation,

$\sqrt{3} \times a = \sqrt{12}$

• taking the factors of 12

$\implies \sqrt{3} \times a = \sqrt{3\times 4}$

$\implies \sqrt{3} \times a = \sqrt{3}\times \sqrt{4}$

$\implies a = \sqrt{4}$

$\implies a = \sqrt{2\times 2}$

$\implies \bold{a = 2\:cm}$

Thus, the length of the edge of the cube is 2 cm.

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