AMC12 2007 B

AMC12 2007 B · Q6

AMC12 2007 B · Q6. It mainly tests Averages (mean), Area & perimeter.

Triangle $ABC$ has side lengths $AB = 5$, $BC = 6$, and $AC = 7$. Two bugs start simultaneously from $A$ and crawl along the sides of the triangle in opposite directions at the same speed. They meet at point $D$. What is $BD$?

三角形 $ABC$ 的边长 $AB = 5$，$BC = 6$，$AC = 7$。两只虫子同时从 $A$ 点出发，沿着三角形的边以相同的速度向相反方向爬行。它们在点 $D$ 相遇。$BD$ 等于多少？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (D)

正确答案：（D）

Solution

Error creating thumbnail: Unable to save thumbnail to destination One bug goes to $B$. The path that he takes is $\dfrac{5+6+7}{2}=9$ units long. The length of $BD$ is $9-AB=9-5=4 \Rightarrow \mathrm {(D)}$

一只虫子爬向 $B$。它所走的路径长度为 $\dfrac{5+6+7}{2}=9$。因此 $BD$ 的长度为 $9-AB=9-5=4 \Rightarrow \mathrm {(D)}$

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