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The triangle on the lft is a 30-60-90 right triangle

The altitude   = 8 *  √3/2  =  4√3  = √48

Since the triangle on the right is a 45 - 45 - 90 right triangle

The altitude  = the base  = √48 =  length of the legs

So..by the Pythagorean Theorem

x  = 

√ [ ( √48 )^2 + ( √48)^2 ]  = 

√96  =

√16 * √6  =

4√ 6