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23 December, 03:49

AB = x + 8

DC = 3x

AD = x + 3

BC = ?

Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs. What is the length of BC?

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  1. 23 December, 03:54
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    Answer: The length of BC is 7

    Step-by-step explanation: Assuming the lengths of the opposite sides of the quadrilateral are congruent, then

    AB=DC and

    AD=BC

    Inputting the values of AB, DC and AD as given in the question:

    x + 8 = 3x ... (1)

    x + 3=? ... (2)

    We have to solve for the value of x to get the actual lengths and thus ascertain BD.

    From equation (1):

    8 = 3x - x

    8 = 2x

    8/2 = x

    Therefore, x = 4.

    If x = 4 then equation (2) would be

    4 + 3 = 7.

    Hence, the actual lengths of the quadrilateral are:

    AB = 4 + 8. DC = 3 (4)

    =12. = 12.

    AD = 4 + 3. AD = BC

    = 7. Therefore, BC = 7.

    Hence, it is confirmed that quadrilateral ABCD is a parallelogram since both the opposite sides are proven to be congruent.
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