Question

D and E are points on sides
AB and AC of A ABC.
and DF ll Bc. if AD= 3 cm & BD = 2cm, find
ar( ∆ADE ) : ar (∆ABC)​

Answer 1

Answer:

at first we prove that two Triangles are similar as angle is common in both the Triangles De and BAC and angle ADC is equal to angle abc De is parallel to BC so angle ADC is equal to angle abc as there are corresponding angles which are equal so by these two methods you get triangle A D is is similar to triangle abc by angle angle criteria

in triangleADE and Triangle ABC

angle A is common

angleADE = angleABC

2 triangles similar by (AA) criteria

now change the two Triangles are equal then the theorem which says that the area of two Triangles in the ratio is equal to asquare of their corresponding sides in the ratios,

so ar( ∆ADE ) : ar (∆ABC)

will be equal to

AD² : AB² = (3)² : (5)² => 9 : 25

given AD=3

AB=AD+BD

3+2 =5

BD = 5 (1)

hope this helped you buddy