Given that triangle ABC was dilated by 50% to create A' B'C' as shown. Picture is missing.
Now we have to find the relationship between older side AC and the newer side A'C' of the triangle.
Word "dilation" basically means to widen or enlarge.
So dilated by 50% means half of the length of AC is added more to AC to produce A'C'.
In other words, A'C'= AC+ 50% of AC
A'C'= AC+ 0.5 AC
A'C'= 1.5 AC
Hence A'C' will be 1.5 times the length of AC.