Question

In triangle pqr a and b are points on sides qr such that they trisect qr prove that area of triangle pqb = 2 ar of pbr

Answer 1

Answer:pqrs is a square .N and m are the mid points of sides Sr and qr respectively .O is a point in diagonal pr such that op=or . Show that ONRM is a square .also find the ratio of are orm and are pqrs

Step-by-step explanation:nm is parallel tosq

NR =SQ

OR=OQ (diagonals are equal)

NM=OQ

OR=NM (diagonals are equal)

all angles are 90degree

ONRM is a square

Similarly ,AONS,PAOB,BOQR are squares

In square , ONRM,

diagonal divided into two equal in areas

ar(ONR)=are(OMR)

PQRS is divided into 4 parts

Ratio is 1:8

arOMRN =1/4 PQRS

2OMR=1/4 PQRS

OMR= 1/8 PQRS

HENCE PROVED