When the question says that triangle ABC ~ triangle DEF, that means the triangles are similar. This means that their proportions are the same. In triangle ABC, side length AB is the equivalent of side length DE in triangle DEF.
Since the proportions must be the same, we can take the known side from triangle ABC, find the equivalent of it on triangle DEF, and find the proportions. We already found that side length AB ~ side length DE. Now we can divide the lengths to find the proportions. 28 / 8 = 3.5 This means that each side on triangle ABC will be 3.5 times greater than the equivalent side on triangle DEF.
The length of AC in triangle ABC is 3.5 times the length of DF in triangle DEF. Side length DF is 10. Multiply 3.5 by 10 to get the length of AC. 3.5 • 10 = 35 So the length of AC is 35 units.
Answer: Side length AC in triangle ABC is 35 units.
