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 . 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 choice .