MathDB

19

Part of 2000 AMC 10

Problems(1)

Right triangles

Source:

2/24/2006
Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the trangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is mm 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) 12m+1(B) m(C) 1−m(D) 14m(E) 18m2\text{(A)}\ \frac1{2m+1}\qquad\text{(B)}\ m \qquad\text{(C)}\ 1-m\qquad\text{(D)}\ \frac1{4m} \qquad\text{(E)}\ \frac1{8m^2}
geometryratiosimilar triangles