Could someone please help me understand how we identified the corresponding sides in this question? Since height and base are interchangeable concepts while dealing with triangles, the explanation in the video didn’t help me completely understand how a set of sides were chosen for the specific cross multiplication.

We know BC. Can we show that CD is related to BC in some way?

AB=5(Pythagorean triplet), and since both angles are 45 so AB=AD, so again by Pythagorean triplet CD=3

I am unable to understand this relationship, I solved it using pythagoras theorem on ABC, ABD and ACD though, but still want to know how the similar triangle concept would work here. Specifically how corresponding sides are identified is what I am having difficulty with.

Sorry my bad, both angles are not 45. Greg wrote that to tell us that we cannot take such an assumption. The answer here is 16/3.

Review the PrepSwift videos on similar triangles - Greg explains how these kinds of problems work.

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