Problem:
Right triangle has leg lengths and . Including and , how many line segments with integer length can be drawn from vertex to a point on hypotenuse ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The area of is . Let be the foot of the altitude from to . By the Pythagorean Theorem, , so , and . Two segments of every length from through can be constructed from to . In addition to these segments and the legs, there is a segment of length from to a point on near , for a total of segments with integer length.
The problems on this page are the property of the MAA's American Mathematics Competitions