Question

length of diagonals of a cube of side a cm is​

Answer 1

Answer:

a√2

Step-by-step explanation:

Use pythagoras theorem, it'll be easy consider a right angle triangle. Then take the length of sides as "a".

Then use pythagoras theorem to find the hypotenuse which will be the diagonal's length

Answer 2

What is the length of a diagonal of a cube whose side is 3 cm?

3 Answers

Parameswaran P N, Studied

Answered June 20, 2019

Diagonal of a cube is the imaginary line between any apex and the farthest apex from that point. This is actually the hypotenuse of a right angled triangle whose one side is the side of the cube and the other side is the diagonal of base of the cube. Here the side of the cube is 3 cm. So the diagonal of the base is to be calculated using Pythegoras theorem. Length ‘h’ of the diagonal of the base will be Square root of 3 squared + 3 squared, is Square root of 18.

Now we can calculate the length ‘l’ of the cube. As explained earlier, it is the diagonal of the right angled triangle whose one side is the side of the cube (3cm) and the other side is the diagonal of the base (Square root of 18). Again applying Pythegoras’ theorem, l squared = 3 squared + square of h, which is square root of 18.

So l squared = 9+18 = 27

Then l = Square root of 27.