2017 AMC 8 Problems/Problem 16
Revision as of 13:56, 2 November 2024 by Megaboy6679 (talk | contribs)
Contents
[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
~megaboy6679
Video Solutions
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.