Final answer:
To find DE, set up the proportion CD/BD = AE/DE using the given ratios 5:8 and 12:DE. Solve for DE to get DE = (12 * 8) / 5, resulting in DE being 19.2 units.
Step-by-step explanation:
To determine the measure of segment DE when triangles ABC and BCD are similar with given side proportions, we need to establish the ratio of corresponding sides and then apply it to find the unknown side. Given that CD:BD is 5:8 and AE:DE is 12:DE, we are looking for the value of DE.
We know that the ratios of corresponding sides in similar triangles are equal, so DE must be in the same ratio to AE as CD is to BD. Therefore, we can set up a proportion: CD/BD = AE/DE. Substituting the known values, we get 5/8 = 12/DE. Solving this proportion for DE gives us DE = (12 * 8) / 5. Hence, DE = 96 / 5 = 19.2 units.