Find x and the measures of the indicated parts

Given:

Two similar triangles AEB and ACD.

To solve for x, we can use ratio and proportion following the rule for similar triangles. 

So,

AE / AD = AB / AC

Substitute values,

AE = AD - DE
AE = 6 - 5
AE = 1

1 / 6 = 2 / (2 + x + 4)

Solve for x 

x = 6

then,

BC = x +4 = 6 + 4 = 10
AC = 2 + x + 4 = 12

Therefore, the measurements of the triangles are:

AE = 1 
BC = 10
AC = 12

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