Question

D and E are respectively the points on the side AB and AC of triangle ABC such that AD=2cm,BD=3cm and BC=7.5cm and DE is parallel to BC. Then length of DE is​

Answer 1

Answer:

In ∆ADE and ABC

angle A common

angle D=B angle ( DE || BC then, d= b)

by AA similarity criteria

∆ADE similar ∆ ABC.

AD/DB = DE / BC

2cm/3cm=DE/7.5cm

DE= 5cm.

if you understand then follow me.

Answer 2

$\huge\sf{\underline{\underline{Solution:}}}$

$\boxed{3\:cm}$

Given :

• A ∆ABC in which DE // BC. AD = 2cm, BD = 3 cm and BC = 7.5 cm.

To find :

• The length of DE

_______________________________________

Since, DE is parallel to BC

→ angle ADE = angle ABC (corresponding angles)

→ angle AED = angle ACB (corresponding angles)

Hence, by AA criterion of similarity,

∆ADE ~ ∆ABC

ratio of corresponding sides of similar triangles are equal.

AD/AB = DE/BC

AB = AD + DB

AB = 2 + 3 = 5 cm

So,

2/5 = DE/7.5

DE = 2/5 × 7.5

DE = 2 × 1.5

DE = 3 cm.

Hence, the length of side DE is 3 cm.