Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that (ii) ar (RQC) = 3/8 ar (ABC)

Q: 7     P and  Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that
              (ii)    \small ar(RQC)=\frac{3}{8}ar(ABC)

Answers (1)

best_answer


In \DeltaRBC, RQ is the median
Therefore ar(\DeltaRQC) = ar(\DeltaRBQ) 
                                   = ar (PRQ) + ar (BPQ)
                                   = 1/8 (ar \DeltaABC) + ar(\DeltaBPQ)  [from eq (vi) & eq (A) in part (i)]
                                   = 1/8 (ar \DeltaABC) + 1/2 (ar \Delta PBC)  [ since PQ is the median of \DeltaBPC]
                                   = 1/8 (ar \DeltaABC) + (1/2).(1/2)(ar \DeltaABC) [CP is the medain of \DeltaABC]
                                   = 3/8 (ar \DeltaABC)

Hence proved.

Posted by

manish

View full answer

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 10 board exams from February 15 to March 18; download date sheet 2025 PDF
anam-khan

CBSE Date Sheet 2025 Live: CBSE Class 10, 12 board exam timetable soon at cbse.gov.in; practical dates
anam-khan

CBSE Date Sheet 2025 Live: CBSE to announce Class 10, 12 board exam dates soon at cbse.gov.in; sample paper

Latest Question