Final answer:
In the parallelogram ABCD, given AE = 3x - 7 and AC = 32, the value of x is found by using the property that diagonals of a parallelogram bisect each other.
After setting up the equation 3x - 7 = 16 and solving for x, we find that x is approximately 7.67.
Step-by-step explanation:
To find the value of x in the parallelogram ABCD, where AE = 3x - 7 and AC = 32, we make use of the property that in a parallelogram, the diagonals bisect each other.
This means that point E is the midpoint of AC.
Therefore, AE equals EC.
Since AC is the entire diagonal with a length of 32 units, AE and EC would each be half of that length.
Now, let's set up our equation:
- AE = EC
- 3x - 7 = 32 / 2
- 3x - 7 = 16
- 3x = 16 + 7
- 3x = 23
- x = 23 / 3
- x = 7.67
Hence, the value of x is approximately 7.67.