Difference between revisions of "2006 AIME I Problems/Problem 7"
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Let... | Let... | ||
| − | *The set of parallel lines | + | *The set of parallel lines... |
| − | :perpendicular to x-axis | + | :be perpendicular to x-axis |
:& cross x-axis at 0, 1, 2... | :& cross x-axis at 0, 1, 2... | ||
*Base of region <math>\mathcal{A}</math> be at <math>x = 1</math>; bigger base of region <math>\mathcal{D}</math> at <math>x = 7</math> | *Base of region <math>\mathcal{A}</math> be at <math>x = 1</math>; bigger base of region <math>\mathcal{D}</math> at <math>x = 7</math> | ||
Revision as of 19:26, 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
Apex of the angle is not on the parallel lines.
Let...
- The set of parallel lines...
- be perpendicular to x-axis
- & cross x-axis at 0, 1, 2...
- Base of region
be at 
; bigger base of region 
at 
- One side of the angle be x-axis.
- The other side be
be at 
; bigger base of region 
Then...
As area of triangle =.5 base x height...
By similar method, 
seems to be 408.
