Difference between revisions of "2006 AIME I Problems/Problem 7"
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An [[angle]] is drawn on a set of equally spaced [[parallel]] [[line]]s as shown. The [[ratio]] of the [[area]] of shaded [[region]] <math> \mathcal{C} </math> to the area of shaded region <math> \mathcal{B} </math> is 11/5. Find the ratio of shaded region <math> \mathcal{D} </math> to the area of shaded region <math> \mathcal{A}. </math> | An [[angle]] is drawn on a set of equally spaced [[parallel]] [[line]]s as shown. The [[ratio]] of the [[area]] of shaded [[region]] <math> \mathcal{C} </math> to the area of shaded region <math> \mathcal{B} </math> is 11/5. Find the ratio of shaded region <math> \mathcal{D} </math> to the area of shaded region <math> \mathcal{A}. </math> | ||
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== Solution == | == Solution == |
Revision as of 20:22, 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
; Lower base of Region
at
- One side of the angle be x-axis.
- The other side be
Then...
As area of triangle =.5 base x height...
By similar method, seems to be 408.