Question

I need help finding the lengths of the triangle and are they similar

Answer 1

The triangles are similar because the corresponding base angles are congruent and they share one vertex.

From here, we can have a proportion in their sides.

`(AD)/(DE)=(AB)/(BC)`

From the problem, AD = 6, DE = 9 and BC = 15

AB will be :

`\begin{gathered} (6)/(9)=(AB)/(15) \\ \text{Cross multiply :} \\ 6(15)=9AB \\ 90=9AB \\ AB=(90)/(9)=10 \end{gathered}`

The answer is 10