S is a point in the interior of a triangle PQR,prove that 2 ( PS + QS + RS) > PQ + QR + RP ?

Asked by nisha_vini29 | 13th Jul, 2017, 10:25: AM

Expert Answer:

begin mathsize 16px style In space triangle space SPQ comma
PS plus QS greater than PQ space space space space space space space space.... left parenthesis straight i right parenthesis
In space triangle space SQR comma
QS plus QR greater than QR space space space space space space space space.... left parenthesis ii right parenthesis
In space triangle space SRP comma
RS plus PS greater than PR space space space space space space space space space space space.... left parenthesis iii right parenthesis
Adding space left parenthesis straight i right parenthesis comma space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis comma space we space get
PS plus QS plus QS plus QR plus RS plus PS greater than PQ plus QR plus PR
rightwards double arrow 2 left parenthesis space PS plus QS plus RS right parenthesis space greater than space PQ plus QR plus RP end style

Answered by Rashmi Khot | 13th Jul, 2017, 11:51: AM