Question: S is any point on the side QR‾ of ΔPQR. Find PQ + QR + RP PS.



A ) greater than 2
B ) less than 2
C ) greater than 1
D ) less than 1

Steps to derive

1 In ΔPQS, PQ + QS > PS
 [Triangle Inequality Theorem.]

2 In ΔPSR, SR + RP > PS
 [Triangle Inequality Theorem.]

3 PQ + (QS + SR) + RP > PS + PS
 [Add the two Inequalities.]

4 PQ + QR + RP > 2PS
 [QS + SR = QR.]

5 PQ + QR + RP PS > 2
 [Divide by PS‾ on both sides.]



Hence the right answer is Option A

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