Question

In the configuration where ABC and EDC are straight lines, EA is parallel to DB, and EC = 11.5cm, DC = 4.6cm, and DB = 3.8cm, what is the length of AE?

Answer 1

To find the length of AE, use the concept of similar triangles to set up a proportion and solve for the unknown length.

Step-by-step explanation:

To find the length of AE, we can use similar triangles. Since EA is parallel to DB, we can see that triangle ACE is similar to triangle DBC. This means that the ratios of corresponding side lengths are equal.

We know DC = 4.6cm, DB = 3.8cm, and EC = 11.5cm. Let x represent the length of AE. Using the similar triangles, we can set up the following proportion: (EC)/(DC) = (AE)/(DB). Solving for AE, we have (11.5cm)/(4.6cm) = x/(3.8cm). Cross-multiplying and solving for x, we find that AE ≈ 9.466cm.