Answer:
7 cm
Explanation:
You want the edge length of a cube whose space diagonal is 7√3 cm.
Face diagonal
The square of the face diagonal of a cube of edge length s is ...
d² = s² +s² = 2s²
Space diagonal
The square of the space diagonal is found by applying the Pythagorean theorem again. The space diagonal is the hypotenuse of a right triangle whose legs are one cube edge and the face diagonal.
D² = s² +d² = s² +2s² = 3s²
D = √(3s²) = s√3
So, we want to find s when D = 7√3:
s√3 = 7√3
s = 7
The edge length of the cube is 7 cm.