Factorize the Box

Geometry Level 3

A cuboid box has a height of \(x\) and a base diagonal (in blue) of length \(2x\).

Considering the triangle \(ABC\) separately, its height (in red) is \(y\), partitioning the (blue) base into \(x-y\) and \(x+y\), as shown above right.

If the volume of the box is 108, what is the value of \(y\)?

Hint: This wiki can help.


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