Question

if triangle ayb - triangle xyz, ab = 5, ay=12, and ay=ax, what is the length of yz?

Answer 1

I’m missing some information / there's an ambiguity in the statement. A few things to confirm:

1. Do you mean triangle AYB is similar to triangle XYZ (AYB ∼ XYZ)?
2. If so, what is the correspondence (which vertex corresponds to which)? For example AYB ∼ XYZ normally means A ↔ X, Y ↔ Y, B ↔ Z.
3. Where is the segment AX coming from? Do you mean the distance from A to X (a point X outside the first triangle) equals AY, or did you mean some side AX in one of the triangles?

With the exact correspondence and the meaning of AX I can give the numeric answer. Right now the data as written is insufficient to determine YZ.

If you intended AYB ∼ XYZ with A↔X, Y↔Y, B↔Z, and AY = 12 equals XY (i.e. corresponding sides AY and XY are equal), then the similarity scale factor is k = XY/AY = 1 and all corresponding sides are equal, so YZ = YB. But you would still need YB to find a number. If instead AB = 5 corresponds to XZ = 5, that only gives XZ, not YZ.

Please confirm the intended similarity/correspondence and what AX means (or upload a diagram) and I’ll finish the solution.