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)


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.

Most Viewed Questions

Related Chapters

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
Buy Now
NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions