Question

D and E are the points on the sides AB and AC respectively of a ∆ABC such that: AD = 8 cm, DB = 12 cm, AE = 6 cm and CE = 9 cm, Prove that BC = 5/2 DE.

Answer 1

It is given that,, and .

We have to prove that

Since clearly

Also, is common in and

So (SAS Similarity)

$$\begin{gathered} \Rightarrow \frac{BC}{DE}=\frac{AB}{AD} \\ \Rightarrow \frac{BC}{DE}=\frac{1}{\left({\displaystyle \frac{AD}{AB}}\right)} \\ \Rightarrow \frac{BC}{DE}=\frac{1}{\left({\displaystyle \frac{2}{5}}\right)}\left({\displaystyle \frac{AD}{AB}=\frac{2}{5}}\right) \\ \Rightarrow \frac{BC}{DE}=\frac{5}{2} \\ \Rightarrow \boxed{BC=\frac{5}{2}DE} \end{gathered}$$