Answer:
9.9 cm
Step-by-step explanation:
The space diagonal is the hypotenuse of the right triangle with legs that are the edge length and the face diagonal length. If x represents the edge length, then we have ...
(√294)² = 14² + x²
x² = 294 -196 = 98
x = √98 ≈ 9.9
The edge length of the cube is about 9.9 cm.
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Comment on the solution
There are (at least) two other ways you can work this problem.
The face diagonal length will be √2 times the edge length, so the edge is ...
(14 cm)/√2 = 7√2 cm ≈ 9.9 cm
The space diagonal is √3 times the edge length, so the edge is ...
(√294)/(√3) = √(294/3) = 7√2 ≈ 9.9 cm
