A diagonal of a cube measures square root 294 cm. the diagonal of a face measures 14cm. what is the length of the cube to the nearest tenth.

  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.

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