Difference between revisions of "2014 AMC 10A Problems/Problem 9"
| Line 14: | Line 14: | ||
{{AMC10 box|year=2014|ab=A|num-b=8|num-a=10}} | {{AMC10 box|year=2014|ab=A|num-b=8|num-a=10}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
| + | |||
| + | [[Category: Introductory Geometry Problems]] | ||
Revision as of 10:00, 20 May 2015
Problem
The two legs of a right triangle, which are altitudes, have lengths 
and 
. How long is the third altitude of the triangle?
Solution 1
We find that the area of the triangle is 
. By the Pythagorean Theorem, we have that the length of the hypotenuse is 
. Dropping an altitude from the right angle to the hypotenuse, we can calculate the area in another way.
Let 
be the third height of the triangle. We have 
See Also
| 2014 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 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. 
