Explanation:
In a parallelogram, opposite sides are equal in length. Therefore, we can set AD equal to CB and DC equal to AB to get two equations:
AD = CB
84 = 5x + 24
DC = AB
28 = 3x - 8
Solving the first equation for x, we get:
84 = 5x + 24
60 = 5x
x = 12
Solving the second equation for x, we get:
28 = 3x - 8
36 = 3x
x = 12
Since both equations give us x = 12, we can conclude that the value of x that makes ADCB a parallelogram is x = 12.
To verify, we can check that the opposite sides are equal in length:
AD = 84 cm
CB = 5x + 24 = 5(12) + 24 = 84 cm
DC = 28 cm
AB = 3x - 8 = 3(12) - 8 = 28 cm
Both pairs of opposite sides have the same length, so ADCB is a parallelogram when x = 12.