Difference between revisions of "2015 AMC 10B Problems/Problem 13"
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Revision as of 17:50, 18 May 2015
Problem
The line 
forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle?
Solution
We find the x-intercepts and the y-intercepts to find the intersections of the axes and the line. If 
, then 
. If 
is 
, then 
. Our three vertices are 
, 
, and 
. Two of our altitudes are 
and 
. Since the area of the triangle is 
, letting 
be our hypotenuse, our final altitude has to be 
. By the Pythagorean Theorem, 
, so the sum of our altitudes is 
.
See Also
| 2015 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 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. 
