Question

solve this question. with the solution

Answer 1

Given:
In triangle PQR,
PM is the median
N is the mid-point of PM
O is the. mid-point of QN

To Prove:
(1) ar(PON)=1/8 ar(PQR)
(2) If ar(OPQ)=12 cm^2 then find ar(PQR)

Proof:

(1)
We know that
=> ar(PRM)=ar(PMQ) ...(i) ; Since, a median divides a triangle into 2 smaller triangles which have equal areas.
=> Similarly,
ar(QMN)=ar(QPN) ...(ii)
and ar(PON)=ar(PQO) ...(iii)
from equations (i), (ii) and (iii);
ar(PON)=1/2 ar(PQN)=1/2 ar(PMQ)=1/2 ar(PRQ) ...(iv)
from equation (iv),
ar(OPN)=1/8 ar(PQR)

(2)
Since, ar(OPQ)=ar(PON)=1/8 ar(PQR)
Therefore,
ar(PON)=12 cm^2=1/8 ar(PQR)
(12×8) cm^2=ar(PQR)
96 cm^2=ar(PQR)

HENCE, PROVED.
Hope this answer helps you.