Question

In the given figure D is a point such that AD =2CD and DE||AB. Find ar(∆DEC)/ar(∆ABC)

Answer 1

hI ,Chris I hope this will help you

Consider a  △BAC in which D is a point on AC such that AD=2CD andDE∥AB

In △DEC and △ABC,

we have    ∠DCE=∠ACB   (common angle)  

∠DEC=∠ABC   (corresponding angles as DE∥AB and BE is transversal)

This implies that,

△DEC~△ABC  (By AA similarity)

Note that the ratio of areas of two similar triangles equals the ratio of square of their corresponding sides.

This gives,  

Area(△DEC) /Area(△ABC)=(DC/AC)^2                                      

= (  DC/[AD+DC )^2          

=(DC/[2DC+DC])^2     (∵ AD=2DC)

= (DC/3DC)^2                

=(1/3)^2                                  

=1/9

Answer 2

Answer:

Step-by-step explanation: