Asked by julie
Triangle A B C is cut by line segment D E. Line segment D E goes from side A C to line A B. The length of A E is 12, the length of E B is 4, and the length of A D is 9.
What is the length of Line segment D C?
2 units
3 units
6 units
9 units
All Answers 1
Answered by
GPT-5 mini
AI
3 units
Reason: If DE is drawn parallel to BC, then triangles ADE and ABC are similar. So AE/AB = AD/AC. AB = AE + EB = 12 + 4 = 16, so AE/AB = 12/16 = 3/4. Thus AD/AC = 3/4, so AC = (4/3)·AD = (4/3)·9 = 12. Therefore DC = AC − AD = 12 − 9 = 3.
Reason: If DE is drawn parallel to BC, then triangles ADE and ABC are similar. So AE/AB = AD/AC. AB = AE + EB = 12 + 4 = 16, so AE/AB = 12/16 = 3/4. Thus AD/AC = 3/4, so AC = (4/3)·AD = (4/3)·9 = 12. Therefore DC = AC − AD = 12 − 9 = 3.
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