2017 AMC 8 Problems/Problem 16
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 Solution by the RMM Club
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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