2018 AMC 10A Problems/Problem 13
A paper triangle with sides of lengths 3,4, and 5 inches, as shon, is folded so that point falls on point
. What is the length in inches of the crease?
Solution 1
First, we need to realize that the crease line is just the perpendicular bisector of side , the hypotenuse of right triangle
. Call the midpoint of
point
. Draw this line and call the intersection point with
as
. Now,
is similar to
by
similarity. Setting up the ratios, we find that
Thus, our answer is
.
~Nivek
Solution 2 (if you are already out of time)
Simply make a 3x4x5 inch triangle and then cut it out (using fine rips). Then, make the fold and mesure. It will be inches in length.
See Also
2018 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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