Question

The length of diagnol of a cube of side a is what?

Answer 1

Answer:

Diagonal of cube=√3a

Answer 2

The length of diagnol of a cube of side a is d = √(3a²) = √3(a)

We have,

The diagonal of a cube follows almost follows the same rule as that of Pythagorean theorem,

⇒ diagonal² = length² + breadth² + width²

taking square root on both sides, we get,

diagonal =  √ ( length² + breadth² + width² )

Let us consider, the length, breadth and width of a cube is given by, x, y and z respectively and the diagonal be given by d, then, we have,

d = √ (x² + y² + z² )

Since, the length breadth and width of a cube are equal, we get,

d = √ (x² + x² + x² )

d = √ (3x²)

given, a is the side of a cube, so, we have,

d = √ (3a²) = √3 × a