Final answer:
Using the properties of similar triangles, we find that the length of AB in triangle ABC is 7.2 cm.
Step-by-step explanation:
The question indicates that triangles ABC and ABD are similar, and it provides the lengths of the sides AD and DC. We are also told that the angle ABD is equal to angle DCB. Because the triangles are similar, the sides are proportional. This allows us to set up a proportion to find the unknown length AB.
Given that AD = 4 cm and DC = 5 cm, the side AC is the sum of AD and DC, which is 9 cm. The ratios of the corresponding sides in similar triangles are equal. Therefore, if AB is x cm in length, then:
AD / AB = DC / AC
Plugging in the given values:
4 / x = 5 / 9
Cross-multiply to solve for x:
4 * 9 = 5 * x
36 = 5x
x = 36 / 5
x = 7.2 cm
So, the length of AB is 7.2 cm.