Difference between revisions of "2003 AMC 10A Problems/Problem 12"
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The line <math>x=y</math> intersects the rectangle at <math>(0,0)</math> and <math>(1,1)</math>. | The line <math>x=y</math> intersects the rectangle at <math>(0,0)</math> and <math>(1,1)</math>. | ||
| − | The area which <math>x | + | The area which <math>x<y</math> is the right isosceles triangle with side length <math>1</math> that has vertices at <math>(0,0)</math>, <math>(1,1)</math>, and <math>(0,1)</math>. |
The area of this triangle is <math>\frac{1}{2}\cdot1^{2}=\frac{1}{2}</math> | The area of this triangle is <math>\frac{1}{2}\cdot1^{2}=\frac{1}{2}</math> | ||
Revision as of 12:14, 28 November 2015
Problem
A point 
is randomly picked from inside the rectangle with vertices 
, 
, 
, and 
. What is the probability that 
?
Solution
The rectangle has a width of 
and a height of 
.
The area of this rectangle is 
.
The line 
intersects the rectangle at and 
.
The area which is the right isosceles triangle with side length that has vertices at , , and .
The area of this triangle is 
Therefore, the probability that is 
See Also
| 2003 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
