Question

Points D and E belong to legs AC, that is BC of the triangle ABC and also AB||DE.If |AB|=20cm, |DE|=15cm, |AC|=16cm, find the length of |AD|.

Answer 1

Given that DE || AB, we can think of CDE and CAB as similar triangles.

This means that corresponding sides are proportional.

We have to find AD.

We can find AD as the difference between the length of CA and the length of CD.

We can write the following proportion:

`(CD)/(CA)=(DE)/(AB)`

Then, we can find CD as:

`\begin{gathered} CD=CA\cdot(DE)/(AB) \\ CD=16\cdot(15)/(20) \\ CD=16\cdot0.75 \\ CD=12 \end{gathered}`

Then, we can find AD as:

`\begin{gathered} AD+DC=AC \\ AD=AC-DC \\ AD=16-12 \\ AD=4 \end{gathered}`

Answer: AD = 4cm