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What is the length of a diagonal of a cube?

80. What is the length of a diagonal of a cube?

1. 3√A
2. 2√3A
3. √3A
4. √6A

Answer

The correct answer is: C) √3A

Explanation

All sides of a cube are the same length. Let "a" represent the length of one side of the cube. A cube's diagonal runs through its center and joins two opposite corners. Within the cube, this diagonal creates the hypotenuse of a right triangle.

The diagonal "D" can be determined using the Pythagorean theorem as follows:

D² = a² + a² + a²

D² = 3a²

Taking both sides square roots:

D = √(3a²) D = √3a