Geometry Tickbox Quiz #11

Why did Greg took the lenght whole lenght of AE as 4n. I understand 4n comes from the ratio of BC/ De which is 1/4. But he could have done as below too

tri ABC/ tri ADE = BC/ DE = AC/AE which can be further written as

5/20 = AC/(AC+CE) [since BC is 5 and DE is 20 as in the figure above]

1/4 = AC/AC +AC/ CE

1/4 = 1+ AC/ CE

Hence, 1/4 - 1 = AC/CE

Due to that -1 AC/ CE is less than 1/4 and hence option B while that is not the answer.

What is wrong in my approch and how is that different from Greg’s approach?