2017 AMC 8 Problems/Problem 16
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[hide]Problem
In the figure below, choose point on so that and have equal perimeters. What is the area of ?
Solution 1
We know that the perimeters of the two small triangles are and . Setting both equal and using , we have and . Now, we simply have to find the area of . Since , we must have . Combining this with the fact that , we get .
Solution 2
Since is less than , must be more than to equate the perimeter. Hence, , so . Therefore, the area of is
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2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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