Problem:
The sides of a triangle have lengths of , and . Find the length of the shortest altitude.
Answer Choices:
A.
B.
C.
D.
E.
Solution:
First notice that this is a right triangle, so two of the altitudes are the legs, whose lengths are and . The third altitude, whose length is , is the one drawn to the hypotenuse. The area of the triangle is . Using as the base and as the altitude, we have
Since the three right triangles in the figure are similar,
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions