Question

In triangle ABC segment DE is parallel to the side AC . (The endpoints of segment DE lie on the sides AB and BC respectively). Find DE, if AC=20cm, AB=17cm, and BD=11.9cm;

Answer 1

Answer:

The length of DE is 14 cm.

Step-by-step explanation:

Given in triangle ABC segment DE is parallel to the side AC . (The endpoints of segment DE lie on the sides AB and BC respectively). we have to find the length of DE.

Given lengths are AC=20cm, AB=17cm, and BD=11.9cm

In ΔBDE and ΔBAC

∠BDE=∠BAC       (∵Corresponding angles)

∠BED=∠BCA       (∵Corresponding angles)

By AA similarity rule, ΔBDE~ΔBAC

∴their corresponding sides are in proportion

⇒ $\frac{BE}{BC}=\frac{BD}{BA}=\frac{DE}{AC}$

⇒ $\frac{BD}{BA}=\frac{DE}{AC}$

⇒ $\frac{11.9}{17}=\frac{DE}{20}$

⇒ $DE=\frac{20\times 11.9}{17}=14cm$