Difference between revisions of "2006 AIME I Problems/Problem 7"
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Revision as of 18:21, 11 March 2007
Problem
An angle is drawn on a set of equally spaced parallel lines as shown. The ratio of the area of shaded region 
to the area of shaded region 
is 11/5. Find the ratio of shaded region 
to the area of shaded region 
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.
