Question
Mon March 09, 2015 By: R K Jha

In triangle PQR, base QR is divided at X such that QX=1/2 XR.Prove that ar (PQX) =1/3 ar (PQR).

Expert Reply
Prasenjit Paul
Tue March 10, 2015
Q X equals 1 half X R L e t space Q X equals x X R equals 2 x Q R equals Q X plus X R equals x plus 2 x equals 3 x L e t space apostrophe h apostrophe space b e space t h e space h e i g h t space o f space t h e space t r a i n g l e s space b e t w e e n space t h e space t w o space l i n e s. fraction numerator A r e a space o f space increment P Q X space over denominator A r e a space o f space increment P Q R space end fraction equals fraction numerator begin display style 1 half end style cross times Q X cross times h over denominator 1 half cross times Q R cross times h end fraction equals fraction numerator x over denominator 3 x end fraction equals 1 third A r e a space o f space increment P Q X equals 1 third A r e a space o f space increment P Q R H e n c e space P r o v e d
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