Since DE is parallel to AC the ratio between the sides of the triangles should be the same.
From the small triangle we notice that 4:5; from the big triangle we notice that 10:AC, since this ratios have to be equatl this means that:
[tex]\begin{gathered} \frac{4}{5}=\frac{10}{AC} \\ AC=\frac{10}{\frac{4}{5}}=\frac{50}{4}=\frac{25}{2}=12.5 \end{gathered}[/tex]
Therefore, AC is 12.5 long.
To find AD we use the same principle. In the small triangle we have that 4:2; for the big triangle we have that 10:(2+AD). Then:
[tex]\begin{gathered} \frac{4}{2}=\frac{10}{2+AD} \\ 2=\frac{10}{2+AD} \\ 2(2+AD)=10 \\ 2+AD=\frac{10}{2} \\ 2+AD=5 \\ AD=5-2 \\ AD=3 \end{gathered}[/tex]
Therefore, AD is 3 long.
