Answer:
The length of AB = 76 units.
Explanation:
We know that Rotations, just like reflections, and translations, are termed isometric.
In other words, these transformations do not alter the size of the figure.
If the size and shape of the figure are not altered, then the figures are termed as congruent.
Given
AB = 5x-14
A'B' = 4x+14
As A'B'C'D' is obtained by rotating ABCD,
so
AB = A'B'
substituting AB = 5x-14 and A'B' = 4x+14
5x-14 = 4x+14
5x - 4x = 14+14
x = 18
Thus,
AB = 5x-14
substitute x = 18
AB = 5(18)-14
AB = 90 - 14
AB = 76
Therefore, the length of AB = 76 units.