Difference between revisions of "2019 AMC 12B Problems/Problem 6"
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How many of such triangles exist? | How many of such triangles exist? | ||
| − | ==Solution== | + | ==Solution 1== |
0 (SuperWill) | 0 (SuperWill) | ||
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| + | ==Solution 2== | ||
| + | |||
| + | Draw segment AB with length 10: | ||
| + | |||
| + | <math>A-------10-------B</math> | ||
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| + | To have area 100, we need the height to be 20, but there is to way to do this when the sum of the other sides is <math>50-10=40</math>. | ||
| + | |||
| + | --mguempel | ||
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==See Also== | ==See Also== | ||
{{AMC12 box|year=2019|ab=B|num-b=5|num-a=7}} | {{AMC12 box|year=2019|ab=B|num-b=5|num-a=7}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 12:56, 14 February 2019
Contents
Problem
Triangle has base 10, area 100, perimeter 50. How many of such triangles exist?
Solution 1
0 (SuperWill)
Solution 2
Draw segment AB with length 10:
To have area 100, we need the height to be 20, but there is to way to do this when the sum of the other sides is 
.
--mguempel
See Also
| 2019 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 5 |
Followed by Problem 7 |
| 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 12 Problems and Solutions | |
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