2007 AMC 12B Problems/Problem 6

Problem

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 $BD$ ?

$\mathrm {(A)}\ 1 \qquad \mathrm {(B)}\ 2 \qquad \mathrm {(C)}\ 3 \qquad \mathrm {(D)}\ 4 \qquad \mathrm {(E)}\ 5$

Solution

One bug goes to $B$ . The path that he takes is $\dfrac{5+6+7}{2}=9$ units long. The length of $BD$ is $92-AB=9-5=4 \Rightarrow \mathrm {(D)}$

2007 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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All AMC 12 Problems and Solutions

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2007 AMC 12B Problems/Problem 6

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