In the figure above, if AB is parallel to DE and DE = 2, what is the

I received a PM requesting that I post a solution.

Triangles that have two angle measurements in common are SIMILAR.
Because AB and DE are parallel:
angle CAB = angle CDE
angle CBA = angle CED
Since triangles ABC and CDE have two angle measurements in common, the two triangles are similar.
When triangles are similar, corresponding sides are in the SAME RATIO.

To make the math easier, let Statement 2 indicate that AC=14 instead of AC=13:



Statements combined:

Case 1:

Here:
BE=10 and BC=14, so BE is \(\frac{5}{7}\) of BC
AC=14 and AB=7
Corresponding sides are in the same ratio:
\(\frac{DE}{AB}= \frac{2}{7}\)
\(\frac{CD}{AC} = \frac{4}{14} = \frac{2}{7}\)
\(\frac{CE}{BC} = \frac{4}{14} = \frac{2}{7}\)
Perimeter of triangle DEC = 4+2+4 = 10

Case 2:

Here:
BE=10 and BC=14, so BE is \(\frac{5}{7}\) of BC
AC=14 and AB=7
Corresponding sides are in the same ratio:
\(\frac{DE}{AB}= \frac{2}{7}\)
\(\frac{CD}{AC} = \frac{4}{14} = \frac{2}{7}\)
\(\frac{CE}{BC} = \frac{5}{17.5} = \frac{10}{35} = \frac{2}{7}\)
Perimeter of triangle DEC = 4+2+5 = 11

Since the perimeter of triangle DEC can be different values, the two statements combined are INSUFFICIENT.