If AE = 3x - 6; DE = 6y - 12, EC = 2x + 2 and EB = 2y + 24 find the values of x and y for which ABCD must be a parallelogram . The drawing is not to scale .
In order for ABCD to be a parallelogram, opposite sides must be equal in length.
Since AD = BC, we have 3x - 6 = 6y - 12.
Simplifying, we have 3x = 6y - 6.
Dividing both sides by 3, we get x = 2y - 2.
Similarly, since AB = CD, we have 2y + 24 = 2x + 2.
Simplifying, we have 2x - 2y = 22.
Rearranging the equation, we get x - y = 11.
We now have a system of equations:
x = 2y - 2
x - y = 11
Solving this system of equations, we can substitute the value of x from the second equation into the first equation:
(2y - 2) - y = 11
2y - 2y - 2 = 11
-2 = 11 + 2
-2 = 13
This is a contradiction, so there are no values of x and y for which ABCD must be a parallelogram.