ANSWER:
AE = 8
DE = 16
STEP-BY-STEP EXPLANATION:
We can determine that the triangles are similar by AAA congruence.
Therefore, we must calculate the ratio with the help of sides AB and CD, like this:
[tex]\begin{gathered} r=\frac{CD}{AB} \\ \text{ replacing} \\ r=\frac{8}{4} \\ r=2 \end{gathered}[/tex]
Now, we can establish the following equation to know the value of x:
[tex]\begin{gathered} r=\frac{ED}{AE} \\ \text{ replacing} \\ 2=\frac{x+12}{3x-4} \\ \text{ solving for x:} \\ 2\cdot(3x-4)=x+12 \\ 6x-8=x+12 \\ 6x-x=12+8 \\ 5x=20 \\ x=\frac{20}{5} \\ x=4 \end{gathered}[/tex]
We replace the value of x to calculate the length of the sides AE and DE:
[tex]\begin{gathered} AE=3\cdot4-4=12-4=8 \\ ED=4+12=16 \end{gathered}[/tex]
