Final Answer:
In ∆ABC, GH is a midsegment parallel to BC. Applying the midsegment theorem, GH is half the length of BC. Given GH = 16, BC = 32. AC is twice the length of GN (midpoint to vertex), so AC = 2 * 16 = 32 units.
The correct option is c. 16 units.
Step-by-step explanation:
In triangle ∆ABC, the length of GH is given as 16 units. To determine the length of AC, we need to understand the relationship between GH and AC within the triangle. GH is a midsegment in ∆ABC, meaning it connects the midpoints of two sides. In particular, GH is parallel to the third side (BC) and is equal to half the length of BC.
Let M be the midpoint of AB, and N be the midpoint of BC. GH is parallel to BC and connects the midpoints of AB and BC. According to the midsegment theorem, GH is half the length of BC, so GH = 1/2 * BC. Therefore, BC = 2 * GH. Given that GH is 16 units, BC is 2 * 16 = 32 units.
Now, since GH is parallel to BC and connects the midpoints M and N, it divides ∆ABC into two smaller triangles: ∆AMG and ∆CNG. The sides of these two triangles are in proportion, so AC is also twice the length of GN. Therefore, AC = 2 * GN.
Since GN is the other half of BC, GN = BC/2 = 32/2 = 16 units. Therefore, AC = 2 * GN = 2 * 16 = 32 units.
In conclusion, the length of AC in ∆ABC is 32 units. Therefore, the correct answer to the given question is option c. 16 units.