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
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
.