Problem:
In the adjoining figure, the triangle is a right triangle with . Median is perpendicular to median , and side . The length of is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since the medians of a triangle intersect at a point two thirds the distance from the vertex and one third the distance from the side to which they are drawn, we can let and . In right triangle , using the fact that a leg of a right triangle is the geometric mean between its projection upon the hypotenuse and the hypotenuse,
Thus , or , and .
