P and Qare the mid-points of sides AB and BCof triangle ABC and R is the mid point of AP, show that

i) ar(PQR)=1/2 ar(ARC)

ii) ar(RQC)= 3/8 ar(ABC)

iii) ar(PBQ)=ar(ARC)

  • 1

i) Take triangle APQ. R is d midpoint of AP. so RQ becomes a medium, rite? Just remember, any median of a triangle divides it into 2 equal area triangles. So ar(PRQ)=ar(RQA) - keep tat in mind.    Now take triangle RCA. Q is d midpoint of AC, so RQ becomes a median. So ar(ARQ) = ar(RQC) or you cn also say tat ar(ARQ) = 1/2 ar(ARC).. as i said above, remember tat the areas of triangle PRQ and ARQ r same? so now, u cn also say ar(PQR)=1/2 ar(ARC).

ii)Dude im nt sure if its 3/8th cus ar(RQC) is only 1/8th of d triangle......so check tat out frm ur teacher..... 3rd one nt so sure.....

Hope u understood d first 1! :D

  • 0
What are you looking for?