Final answer:
Using the properties of similar triangles in triangle ABC with DE parallel to BC, the length of AE is calculated as 2.5 cm based on the proportionality of sides.
Step-by-step explanation:
In the given question, triangle ABC has points D and E on the sides AB and AC respectively, with DE parallel to BC. Using the properties of similar triangles, we can determine the length of segment AE. The length of AD is given as 5 cm, the length of DB as 8 cm (making the total length of AB 5 cm + 8 cm = 13 cm), and the length of AC as 6.5 cm. Since DE is parallel to BC and D and E divide the sides of the triangle proportionally, the ratios of corresponding sides of the similar triangles are equal. Therefore, the ratio of AD to AB (which is 5/13) is equal to the ratio of AE to AC.
Setting up the proportion: AE / 6.5 cm = 5 cm / 13 cm
By cross-multiplying we find that: 13 cm × AE = 5 cm × 6.5 cm
AE = (5 cm × 6.5 cm) / 13 cm = 32.5 cm / 13 cm = 2.5 cm.
Thus, the length of AE is 2.5 cm.