Right Triangle Parallel Lines
Source:
March 21, 2008
geometryratiosimilar triangles
Problem Statement
Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is times the area of the square. The ratio of the area of the other small right triangle to the area of the square is
(A)\ \frac {1}{2m \plus{} 1} \qquad (B)\ m \qquad (C)\ 1 \minus{} m \qquad (D)\ \frac {1}{4m} \qquad (E)\ \frac {1}{8m^2}