Answer:
The length of DE is 7.2 units.
Explanation:
In the figure:
[tex]\begin{gathered} CD=FG+GE\text{ (Opposite sides of a rectangles)} \\ 12=FG+7 \\ FG=12-7 \\ FG=5 \end{gathered}[/tex]
Triangles CBA and AGE are similar, thus:
[tex]\begin{gathered} \frac{CB}{BA}=\frac{AG}{GE} \\ \frac{3}{5}=\frac{AG}{7} \\ AG\times5=3\times7 \\ AG=\frac{21}{5} \\ AG=4.2\text{ units} \end{gathered}[/tex]
Thus, we have that:
[tex]\begin{gathered} BF=AG=4.2 \\ DE=CB+BF\text{ (Opposite sides of a rectangle)} \\ DE=3+4.2 \\ DE=7.2\text{ units} \end{gathered}[/tex]
The length of DE is 7.2 units.
