Question

In triangle ABC , D is the mid-point of side BC, E is the mid point of AD, F is the mid point of BE, and G is the mid point of FC. If the ratio of ar * (Delta*A * B * C) to ar(AEFG) is p: q, where p and q are co-primes then find p + q .​

Answer 1

Step-by-step explanation:

R.E.F image

Given,

'D' is the midpoint of side BC.

'G' is the centroid of

△ ABC.

also given,

to find out,

ar(△ABD)

ar(△AGB)

as 'D' is the midpoint of BC

we get,BD=DC

'G' is the centroid of △ABC.

since we know that,

centroid divides a median in 2:1 ratio

we get,

AG:GD=2:1

as in the given figure ,

the two triangles △ ABD and △AGB

have the same base of line and the

common verier ,so their ratio of

the triangles area will be equal to their

base ratio

so we get,

ar(△ABD)

ar(△AGB)

=

AD

AG

⇒

AG+GD

AG

⇒

2+1

2

⇒

3

2

ar(△ABD)

(△AGB)

=

3

2