Similar triangle problem - Geometry

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?

@ganesh can you kindly help share your views on the above of where I’m going wrong.

\frac{1}{a + b} \neq \frac{1}{a} + \frac{1}{b}

Also: don’t ping people unnecessarily.

@Leaderboard Thank you for clarifying. Also, I didnot ping anyone individually via DM on this problem till now, just tagged Ganesh. Not sure, if pinging is equivalent to tagging.

It is here.