Final answer:
To find the length CD in triangle BCD, we can use the concept of similar triangles. By setting up a proportion between the corresponding sides of triangle ABC and triangle BCD, we can find that the length of CD is 4 cm.
Step-by-step explanation:
To find the length CD, we can use the concept of similar triangles. Since triangle ABC is similar to triangle BCD, the corresponding sides are proportional. Let's assume the length of AB is x and the length of BC is y. Therefore, the length of CD is also y.
Since we know the length of AB is 4 cm, we can set up a proportion: AB/BC = BC/CD. Substituting the values, we have 4/x = x/y.
By cross-multiplying, we get 4y = x^2. Since AB is 4 cm, AB is equal to x. Therefore, we have 4y = 4^2, which simplifies to y = 4 cm.