Question

What is the length of AC?A. 32 unitsB. 16 unitsC. 24 unitsD. 48 units

Answer 1

Since the segment GH is created by the midpoints of sides AB and BC, so the sides AC and GH are parallel and the triangles ABC and GBH are similar.

Therefore, we can write the following proportion:

`\begin{gathered} (GB)/(AB)=(GH)/(AC) \\ (GB)/(2\cdot GB)=(16)/(AC) \\ (1)/(2)=(16)/(AC) \\ AC=2\cdot16 \\ AC=32\text{ units} \end{gathered}`

So the correct option is A.