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PLEASE HELP!!!!!!!

Points A and C are vertices of a cube with a side length of 2 cm, and B is the point of the intersection of the diagonals of one face of the cube, as shown below.

Determine the length of CB.

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sqdancefan

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Answer:

  CB = √6 cm

Step-by-step explanation:

The diagonal of a square is √2 times the edge length, so the length AB will be (1/2)√2(2 cm) = √2 cm.

Then the length CB is given by the Pythagorean theorem as ...

  CB = √(AC^2 +AB^2) = √((2 cm)^2 + (√2 cm)^2) = √(4 +2) cm

  CB = √6 cm

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