Question

In the given figure, DE || BC in ∆ABC such that BC = 8 cm, AB = 6 cm and DA = 1.5 cm. Find DE.

Answer 1

Given: In ∆ABC, DE || BC. BC = 8 cm, AB = 6 cm and DA = 1.5 cm.

To find: DE

In ∆ABC and ∆ADE

\[\angle B = \angle ADE \left( \text{Corresponding angles} \right)\]
\[\angle A = \angle A \left( \text{Common} \right)\]
\[ \therefore ∆ ABC~ ∆ ADE \left( \text{AA Similarity} \right)\]

So,

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

`8/(DE)=6/1.5`

`DE= (8xx1.5)/6`

`DE= 2  cm`