Question

In ∆ABC , B-D-C and BD = 6cm, DC=4cm. What is the ratio of A(∆ABC) to A(ACD) ?

Answer 1

Answer:

△ ABC and △ CAD

∠ABD=∠CAD (Given)

∠ACB=∠ACD (Common angle)

∠CAB=∠CDA (Third angle)

Hence, △ABC∼△DAC (AAA rule)

Ar.△BCA

Ar.△ACD

=

AB

2

AD

2

(Ratio of areas of similar triangles is equal to ratio of square of corresponding sides)

Ar.△BCA

Ar.△ACD

=

5

2

4

2

Ar.△BCA

Ar.△ACD

=

25

16