In the diagram $AB=6\,\mathrm{cm}, \,AC=10\,\mathrm{cm}, \,DE=4\,\mathrm{cm}$. What is the length of $AD$ (in $\mathrm{cm}$)?
I am searching for concept used to find out length of triangle as per the diagram in attachment. I do have an answer from worksheet as 14/3 but cannot find reason behind it. Shall appreciate if someone can advise on this. Thanks!
You can find $\overline{BC} = \sqrt{10^2-6^2} = 8$, and since $\Delta DEC$ is similar to $\Delta ABC$, we have $\overline{DC} = \frac{16}{3}$ (and $\overline{EC} = \frac{20}{3}$). So $\overline{AD} = 10 - \frac{16}{3} = \frac{14}{3}$.