Is the short cut just to realize that the ratio of XG to YT is the same as the ratio of the length of the sides (12 to 9)? Or is it just a coincidence that the ratios are the same?

Thank you

I would say it is just a coincidence. For diagrams like this, we cannot be to quick to judge. Just because point X and point Y seems to be skewed towards the right, it does not mean it is (unless stated by the question).

For all we know, point X and Y could be in the middle of both squares, in that case the answer would be 6/4.5 (again the question never implied that we needed integers.

I would approach this question in steps, to not lose my chain of thought.

- Area of large square divide by smaller square 16/9 ← we now know the ratio multiplier
- Area of smaller triangle * ratio multiplier = area of larger triangle
- [length YT * 9 * 1/2] * [16/9] = [length XG * 12 * 1/2]
- Simple algebra will result in: Length XG/Length YT = (9/2)
*(16/9)*(2/12) = 4/3

Thank you! I appreciate the long explanation!