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ABCDE is a Pentagon with BE parallel to CD and BC parallel to DE. BC is perpendicular to CD. if the perimeter of ABCDE is 21cm. Find the value of x and y.

  • maths - ,

    Since BC|| DE and BE || CD with BC bisects CD, BCDE is a rectangle.

    : opp sides are equal

    i.e, BE = CD : x + y = 5 ......(1)

    DE = BC : x - y .......(2)

    Since perimeter of ABCDE is 21

    : AB + BC + CD + DE + EA = 21
    3 + x - y + x + y + x - y + 3 = 21

    6 + 3x - y = 21
    3x - y = 15

    Adding (1) and (2) we get
    4x = 20
    x = 20/4
    x = 5

    Putting x = 5 in (1)
    (5) + y = 5
    y = 5 - 5
    y = 0

    : x = 5 , y = 0

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