Difference between revisions of "1956 AHSME Problems/Problem 43"
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(If you see any cases I missed out, edit them in.) | (If you see any cases I missed out, edit them in.) | ||
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| + | ==Video Solution== | ||
| + | https://youtu.be/LYFaYLiLTXE | ||
| + | |||
| + | ~Lucas | ||
==See Also== | ==See Also== | ||
{{AHSME 50p box|year=1956|num-b=42|num-a=44}} | {{AHSME 50p box|year=1956|num-b=42|num-a=44}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 16:29, 19 September 2022
Contents
Problem 43
The number of scalene triangles having all sides of integral lengths, and perimeter less than 
is:
Solution
We can write all possible triangles adding up to 12 or less
![\[(2, 4, 5)=11\]](http://latex.artofproblemsolving.com/2/b/b/2bbc03127e4c72fcaad5be80302568ca35e99e88.png)
![\[(3, 4, 5)=12\]](http://latex.artofproblemsolving.com/a/b/3/ab37dcd4ceec9d18ccec45f590018d0f7ce958ef.png)
![\[(2, 3, 4)=9\]](http://latex.artofproblemsolving.com/d/d/e/dde94fcb1ea507def8fcdac780fa153011918fb4.png)
This leaves 
scalene triangles.
-coolmath34
-rubslul
(If you see any cases I missed out, edit them in.)
Video Solution
~Lucas
See Also
| 1956 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 42 |
Followed by Problem 44 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
