Answer: 22.5 / F
Step-by-step explanation:
Looking at the image, you can see that the triangles GFH and BAC are similar.
These pairs of sides correspond with each other
BA and GF (BA * factor = GF)
AC and FH (AC * factor = FH)
CB and HG (CB * factor = HG)
To find the ratio between these two triangles, you can divide GF by BA (13.5/9) to get 1.5 or FH by AC (18/12) to get 1.5. You end up with the same ratio both ways because the triangles are similar
Now that we established that triangle GFH has sides that are 1.5 times longer than triangle BAC, we can find the length of HG using the length of its corresponding side CB and the ratio (CB * factor = HG).
15 * 1.5 = 22.5 = HG
also answer choice F in the picture
