Difference between revisions of "2006 AIME I Problems/Problem 7"
(→Solution) |
|||
Line 7: | Line 7: | ||
== Solution == | == Solution == | ||
− | |||
Let: | Let: | ||
The set of parallel lines... | The set of parallel lines... |
Revision as of 19:21, 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.