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 11:00, 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.