Question

Upper DeltaABC and Upper DeltaADE are similar. Find the length of side CA.
DeltaCB 2
DeltaED 9
DeltaBA 2
DeltaED 6
2

Answer 1

I’m missing a clear set of given lengths — the list you posted has ED twice (9 and 6) and it’s not stated which segment lengths correspond to which points in the two triangles. Can you confirm the exact given lengths (for AB, BC, AD, DE, AE, etc.)?

Meanwhile, here is the general method you can use once the numbers are fixed:

If triangles ABC and ADE are similar with the correspondence A↔A, B↔D, C↔E, then corresponding sides are proportional:
AB/AD = BC/DE = AC/AE.

So to find AC you can use either ratio:
- AC = AE · (BC/DE), if AE, BC, DE are known; or
- AC = AB · (AE/AD), if AB, AE, AD are known.

Example: if BC = 2 and DE = 6, the scale factor BC/DE = 2/6 = 1/3, so AC = (1/3)·AE. If you also know AE (or AD and AB so you can get AE), you can compute AC numerically.

Tell me the correct values for the listed segments and I’ll compute CA for you.