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.
