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emmainna [20.7K]
3 years ago
9

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 ne

arest tenth.
Mathematics
2 answers:
Andrei [34K]3 years ago
8 0

Answer:

9.9

Step-by-step explanation:

i just took the test

s2008m [1.1K]3 years ago
4 0

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.

_____

<em>Comment on the solution</em>

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

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