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