Question

if triangle ABC DE is parallel to BC and AD/DB=2/3 calculate the value of area of trapezium DECB/AREA of the triangle of ABC

Answer 1

ANSWER

In △ABC, we have

DE∣∣BC

⇒

AD

AB

=

AE

AC

Thus, in triangles ABC and ADE, we have

AD

AB

=

AE

AC

and, ∠A=∠A

Therefore, by SAS-criterion of similarity, we have

△ABC∼△ADE

⇒

AD

AB

=

DE

BC

.......(i)

It is given that

AD

AB

=

3

2

⇒

AD

DB

=

2

3

⇒

AD

DB

+1=

2

3

+1

⇒

AD

DB+AD

=

2

5

⇒

AD

AB

=

2

5

.............(ii)

From (i) and (ii), we get

DE

BC

=

2

5