Answer:
We can use the properties of the diagonals of a parallelogram to find the value of x.
In a parallelogram, the diagonals bisect each other, so we have:HD = DF
Substituting the given expressions for HD and DF, we get:x^2 - 34 = x^2 - 4xSimplifying this equation, we can cancel out the x^2 terms on both sides and get:-34 = -4xDividing both sides by -4, we get:x = 8.5
Therefore, the value of x is 8.5. We can use this value to find the lengths of HD and DF:
HD = x^2 - 34 = 8.5^2 - 34 = 44.75
DF = x^2 - 4x = 8.5^2 - 4(8.5) = 44.75
Therefore, HD = DF = 44.75.