• Answer of this question

    Perimeter of a rhombus is 146 cm and length of one of its diagonals is 48 cm. Find the length of its other diagonal.
    Davneet Singh's image
    Davneet Singh

    Hi Rishav,

    Rhombus has all 4 sides equal,

    So, Perimeter = 4 x Side of rhombus

    146 = 4 x Side of Rhombus

    146/4 = Side of Rhombus

    36.5  = Side of Rhombus

    Side of Rhombus = 36.5 cm

    Perimeter of a rhombus is 146 cm and length of one of its diagonals is 48 cm. Find the length of its other diagonal.PNG

    Thus, AB = BC = CD = AD = 27.5 cm

    And given Diagonal BD = 55 cm

    We need to find AC

     

    Also, Diagonals of rhombus bisect each other at right angles,

    Thus, angle AOB = 90

    and OB = OD = BD/2 = 55/2 = 27.5

     

    Now, AOB is a right angled triangle,

    By Pythagoras Theorem

    AB2 = AO2 + OB2

    (36.5)2 = AO2 + (27.5)2

    (36.5)2 - (27.5)2 = AO2

    AO2 = (36.5)2 - (27.5)2

    AO2 = (36.5 - 27.5) (36.5 + 27.5)

    AO2 = (9) (64)

    AO = (3) (8)

    AO = 24

     

    Thus, AC = 2AO = 2(24) = 48 cm

    Written on March 23, 2017, 12:06 p.m.

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