2006 AIME I Problems/Problem 7

Revision as of 19:21, 11 March 2007 by K1c2h2o (talk | contribs) (Solution)

Problem

An angle is drawn on a set of equally spaced parallel lines as shown. The ratio of the area of shaded region $\mathcal{C}$ to the area of shaded region $\mathcal{B}$ is 11/5. Find the ratio of shaded region $\mathcal{D}$ to the area of shaded region $\mathcal{A}.$



Solution

Let:

  The set of parallel lines...
     perpendicular to x-axis &
     cross x-axis at 0, 1, 2...
  The base of area A is at x = 1.
  One side of the angle be the x-axis.
  The other side be y = x-h...
     as point of the angle isn't on
     parallel lines

Then...

Area C / Area B = 11 / 5 = [.5(5-h)^2 - .5(4-h)^2] / [.5(3-h)^2 - .5(2-h)^2] Thus h = 5/6

By similar method, D/A seems to be 408.

See also