If necessary I can do a drawing, anyone helping please ask if you wish me to draw a similar triangle for this explantion.

We start with an equilatral triangle and label the vertices top A, bottom left B and bottom right C.

We draw a parallel line to BC.

We have;

A to Y 2 units, Y to B 1 unit.

I should think that A to Z will also be 2 units and Z to C 1 unit.

I am asked to find the lengths of the parallels lines using ratios, however the following idea has too many unknowns I think and am wondering if another method is available?

(AY) / (YB) = (YZ) / (BC) = (2) / (1) = (x) / (x)

The problem here is that I can't solve the problem with more than one uknown?

Any ideas please