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2000 AMC 12 Question 21

AMC12 · 2000 AMC 12

Question 21

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 $m$ times the area of the square. What is the ratio of the area of the other small right triangle to the area of the square?
  1. $\dfrac{1}{2m + 1}$
  2. $m$
  3. $1 - m$
  4. $\dfrac{1}{4m}$
  5. $\dfrac{1}{8m^2}$