2008 AMC 10B Problems/Problem 6
Contents
Problem
Points and lie on . The length of is times the length of , and the length of is times the length of . The length of is what fraction of the length of ?
Solution 1
Let . Then and . From this system of equations, we obtain . Adding to both sides of the second equation, we obtain . Thus,
Solution 2
Let and . Therefore, and , as shown in the diagram(the labels on the bottom are for that line segment while the labels on the top are from one point to the left to one point to the right).
From this, we can see that , and since . Now, our ratio is . We can split this into 2 fractions:
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See also
2008 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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All AMC 10 Problems and Solutions |
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