What is the value of x for question 5?

Theorem:
If a segment joins the midpoints of two sides of a triangle, then that segment is parallel to and half the length of the third side.

The right side of the big triangle is split into two segments. The segments are congruent.
The left side of the big triangle is also split into two segments. Those two segments are congruent.

The segment with length 16 joins the midpoints of two sides of the big triangle, so we can apply the theorem above.

The segment with length 16 is half the length of the segment with length 8x.

8x = 2 * 16

8x = 32

x = 4