Pors is quadrilateral.show that pq+qr+sr+ps>2(pq+qs)
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Posted by Satendra Yadav 6 years, 5 months ago
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Sia ? 6 years, 5 months ago
OP + OQ > PQ . . ..[Sum of any two sides of a triangle is greater than third side] . . .(1)
In {tex}\triangle{/tex}OQR,
OQ + OR > QR .[Sum of any two sides of a triangle is greater than third side] . . .(2)
In {tex}\triangle{/tex}ORS,
OR + OS > RS .[Sum of any two sides of a triangle is greater than third side] . . .(3)
In {tex}\triangle{/tex}OSP,
OS + OP > SP .[Sum of any two sides of a triangle is greater than third side] . . .(4)
Adding (1), (2), (3) and (4)
2(OP + OQ + OR + OS) > PQ + QR + RS + SP
2(PR + QS) > PQ + QR + RS + SP . . .[As OP + OR = PR and OQ + OS = QS]
PQ + QR + RS + SP < 2(PR + QS)
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