In a triangle PQR,
PQ=PR and the lengths of the sides are integers.
E is the midpoint of QR.
QE,PE and PQ are in arithmetic progression.
Then what is the least possible value of perimeter of the triangle PQR?
 

Asked by Susan fletcher | 26th May, 2014, 11:06: AM

Expert Answer:

G i v e n comma space Q E comma space P E comma space P Q space a r e space i n space A P space w h i c h space m e a n s P E equals fraction numerator Q E plus P Q over denominator 2 end fraction Q E equals fraction numerator Q R over denominator 2 end fraction S o comma space 2 P E space equals space fraction numerator Q R over denominator 2 end fraction plus P Q 4 P E equals space 2 P Q plus Q R ;  P e r i m e t e r space o f space t r a i n g l e space P Q R space i s space P Q space plus thin space Q R space plus thin space P R b u t space g i v e n space P Q space equals space P R  S o space p e r i m e t e r space b e c o m e s space 2 P Q space plus thin space Q R  f r o m space a b o v e space e q u a t i o n space w e space h a v e space 2 P Q space plus thin space Q R space equals space 4 space P E  S o space m i n i m u m space v a l u e space o f space p e r i m e t e r space i s space 4 space P E space w h i c h space i s space 4 space t i m e s space m e d i a n. space

Answered by Dharma Teja | 4th Jun, 2014, 03:27: PM

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