Final answer:
To find the length of AE, we can use the property of similar triangles. By setting up a proportion using the given information, we can solve for AE.
Step-by-step explanation:
DE is drawn parallel to the base BC of triangle ABC and meets AB at D and AC at E. Given that AC/AB = 4 and CE = 2 cm, we need to find the length of AE.
Since DE is parallel to BC, we can use the property of similar triangles to solve this problem. Since AB = 4AC, we can write the proportion: AE/EC = AB/BC = 4/1. Substituting the given values, we have AE/2 = 4/1, which simplifies to AE = 8 cm.