AMC8 2000

AMC8 2000 · Q15

AMC8 2000 · Q15. It mainly tests Triangles (properties), Area & perimeter.

Triangle ABC, ADE, and EFG are all equilateral. Points D and G are midpoints of AC and AE, respectively. If AB = 4, what is the perimeter of figure ABCDEFG?

三角形 ABC、ADE 和 EFG 均为等边三角形。点 D 和 G 分别是 AC 和 AE 的中点。若 AB = 4，则图形 ABCDEFG 的周长是多少？

(A) 12 12

(B) 13 13

(D) 18 18

(E) 21 21

Answer

Correct choice: (C)

正确答案：（C）

Solution

The large triangle $ABC$ has sides of length $4$. The medium triangle has sides of length $2$. The small triangle has sides of length $1$. There are $3$ segment sizes, and all segments depicted are one of these lengths. Starting at $A$ and going clockwise, the perimeter is: $AB + BC + CD + DE + EF + FG + GA$ $4 + 4 + 2 + 2 + 1 + 1 + 1$ $15$, thus the answer is $\boxed{C}$

大三角形 $ABC$ 边长为 $4$。中等三角形边长为 $2$。小三角形边长为 $1$。有 $3$ 种线段长度，图中所有线段均为这些长度之一。从 A 顺时针开始，周长为： $AB + BC + CD + DE + EF + FG + GA$ $4 + 4 + 2 + 2 + 1 + 1 + 1$ $15$，答案 $\boxed{C}$。

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