Question

in triangle abc p,q,r are the mid point area of a triangle Pqr:16cm2 find the area of abc

Answer 1

Answer:

Step-by-step explanation:

Answer:

area of triangle ABC is

Step-by-step explanation:

Given  triangle ABC ,P, Q,and R are the midpoint of sides AB, bc and AC respectively if . we have to find the ar(ABC).

In ΔABC, P and Q are the mid points of sides AB and BC ∴ by mid-point theorem PQ is parallel to AC and equal to half of AC.

⇒ PQ=AR and PQ||AR and also PQ=RC and PQ||RC

⇒ QPAR and PQRC both are parallelogram

As One diagonal of a parallelogram divides the parallelogram into 2 congruent triangles of equal area.

⇒ ar(PQR)=ar(APR) and ar(PQR)=ar(QRC)   →   (1)

Similarly, In ΔABC, P and R are the mid points of sides AB and AC  ∴ by mid-point theorem PR is parallel to BC and equal to half of BC

⇒ PR=BQ and PR||BQ

⇒ PRBQ is a parallelogram

As One diagonal of a parallelogram divides the parallelogram into 2 congruent triangles of equal area.

⇒     →  (2)

From eq (1) and (2),  

Hence area of triangle ABC is 72cm^2