Difference between revisions of "2020 AMC 12A Problems/Problem 17"
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==Solution 1== | ==Solution 1== | ||
| − | Let the <math>x</math>- | + | Let the left-most <math>x</math>-coordinate be <math>n.</math> |
Realize that by the shoelace formula the area of the triangle must be <math>-\ln{n}+\ln{n+1}+\ln{n+2}-\ln{n+3}.</math> That equals to <math>\ln\frac{(n+1)(n+2)}{n(n+3)}.</math> | Realize that by the shoelace formula the area of the triangle must be <math>-\ln{n}+\ln{n+1}+\ln{n+2}-\ln{n+3}.</math> That equals to <math>\ln\frac{(n+1)(n+2)}{n(n+3)}.</math> | ||
Revision as of 01:03, 2 February 2020
Problem 17
The vertices of a quadrilateral lie on the graph of 
, and the 
-coordinates of these vertices are consecutive positive integers. The area of the quadrilateral is 
. What is the -coordinate of the leftmost vertex?
Solution 1
Let the left-most -coordinate be 
Realize that by the shoelace formula the area of the triangle must be 
That equals to 
The -intercept is 
~lopkiloinm.
