16) C

This involves the use of rule of similarity.

Triangles ABC and ADE are similar.

AB/BC = DA/DE

4/x = x/(x+3)

4x + 12 = x²

x² – 4x – 12 = 0

Factorising, we get:

x² – 6x + 2x – 12

x (x – 6) + 2 (x – 6)

(x – 6) (x + 2)

So x = 6 or x = -2

Since the length cannot be negative, x = 6.

Since DE = x + 3, DE = 6 + 3 = 9 cm