Question

In triangle ABC segment DE is parallel to the side AC. (The endpoints of segment DE lie on the sides AB and BC respectively).

Find DE, if AC=18dm, AB=15dm, and AD=10dm.

Answer 1

6 dm

Explanation:

Triangle DBE is similar to triangle ABC, so their side lengths are proportional.

DE/AC = DB/AB

The length of DB can be found from ...

DB +AD = AB

DB = AB -AD = (15 -10) dm = 5 dm

So, we can fill in the proportion:

DE/(18 dm) = (5 dm)/(15 dm)

DE = (18 dm)·(1/3) . . . . . . . . . . simplify, multiply by 18 dm

DE = 6 dm

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