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ABCD is quadrilateral. Is AB+BC+CD+DA<2 (AC+BD)

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ABCD is quadrilateral. Is AB+BC+CD+DA<2 (AC+BD)

    • Posted by Monalisa Sahu 2 years, 8 months ago

    CBSE > Class 07 > Mathematics
    • 1 answers

    Preeti Priya 2 years, 8 months ago

    In triangle AOB, AB < OA + OB.........(1) In triangle COD, CD < OC + OD........(2) In triangle AOD, DA < OD + OA.........(3) In triangle COB, BC < OC + OB........(4) Adding equation (1), (2), (3) and (4) we get, AB + BC + CD + DA < OA + OB + OC + OD + OD + OA + OC + OB = AB + BC + CD + DA < 2OA + 2OB + 2OC + 2OD = AB + BC + CD + DA < 2(OA + OB) + 2(OC + OD) = AB + BC + CD + DA  < 2(AC + BD) [From diagram OA + OB = AC and OC + OD = BD] Yes, AB + BC + CD + DA <  2(AC + BD) is true.

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