Question

The area of the diagonal section of a cube is equal to 36Ì2. Determine the edge and the diagonal of the cube.? please help me thank you :)

Answer 1

The answer is the edge of the cube is 6 and the diagonal of the cube is 6√3
 
The diagonal section of a cube is a rectangle with sides a and x, where a is the edge of the cube, and x is a diagonal of a side of the cube. Therefore, the area of a diagonal section (A) is:
A = a * x
Now, a = ? and x = ?, but we know that the side of the cube is square and its diagonal is x = a√2.

So, we have:
A =  36√2
a = ?
x = a√2

Let's substitute all parameters in the formula for the area:
A = a * x
36√2 = a * a√2

Divide both sides by √2:
36 = a * a
36 = a²
⇒ a =√36 = 6

The diagonal of the cube can be calculated by using the formula: d = a√3
Since a = 6, then:d = 6√3

Therefore, the edge of the cube is 6 and the diagonal of the cube is 6√3.