Problem:
The two legs of a right triangle, which are altitudes, have lengths and . How long is the third altitude of the triangle?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The area of the triangle is . By the Pythagorean Theorem, the hypotenuse has length . The desired altitude has length .
The problems on this page are the property of the MAA's American Mathematics Competitions