Question

If the length of the diagonal of a cube is \(2\sqrt{3}\) cm, then the length of its edge is

• A. 2 cm
• B. \(2\sqrt{3}\) cm
• C. 3 cm
• D. 4 cm

Hint:

Remember the formula for the diagonal of a cube: \(d = a\sqrt{3}\). Don't confuse it with the diagonal of a face of the cube, which is \(a\sqrt{2}\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The diagonal of a cube is the line segment connecting two opposite vertices. Its length is related to the length of the cube's edge by a specific formula.

Step 2: Key Formula or Approach:
The formula for the length of the diagonal (\(d\)) of a cube with edge length (\(a\)) is:
\[ d = a\sqrt{3} \] We are given \(d\) and need to solve for \(a\).

Step 3: Detailed Explanation:
We are given that the diagonal, \(d = 2\sqrt{3}\) cm.
Substitute this into the formula:
\[ 2\sqrt{3} = a\sqrt{3} \] To find \(a\), divide both sides by \(\sqrt{3}\):
\[ a = \frac{2\sqrt{3}}{\sqrt{3}} \] \[ a = 2 \] The length of the edge is 2 cm.

Step 4: Final Answer:
The length of its edge is 2 cm.