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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?
- 3√A
- 2√3A
- √3A
- √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