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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  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

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

the answer is d

step-by-step explanation: