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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

  • maths -

    Since BC || DE and BE || CD with B perpendicular to CD , BCDE is a rectangle

    => opp sides are equal
    BE=CD => x+y=5.....(1)
    DE=BC => x-y

    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
    x-y = 5.....(2)
    Adding (1) and (2) we get
    2x = 10
    x= 10/2
    x= 5

    Put x=5 in eq (1)
    (5)+y=5
    Y= 5-5
    Y=0

    Hence, x=5 and y=0

  • maths -

    Since BC || DE and BE || CD with B perpendicular to CD , BCDE is a rectangle

    => opp sides are equal
    BE=CD => x+y=5.....(1)
    DE=BC => x-y

    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
    x-y = 5.....(2)
    Adding (1) and (2) we get
    2x = 10
    x= 10/2
    x= 5

    Put x=5 in eq (1)
    (5)+y=5
    Y= 5-5
    Y=0

    Hence, x=5 and y=0

  • maths -

    Since BC || DE and BE || CD with B perpendicular to CD , BCDE is a rectangle

    => opp sides are equal
    BE=CD => x+y=5.....(1)
    DE=BC => x-y

    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
    x-y = 5.....(2)
    Adding (1) and (2) we get
    2x = 10
    x= 10/2
    x= 5

    Put x=5 in eq (1)
    (5)+y=5
    Y= 5-5
    Y=0

    Hence, x=5 and y=0

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