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2023 LMT Fall
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2023 LMT Fall
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(1)
2023 Fall Theme p1C
Source:
12/23/2023
How many distinct triangles are there with prime side lengths and perimeter
100
100
100
?Proposed by Muztaba SyedSolution.
0
\boxed{0}
0
As the perimeter is even,
1
1
1
of the sides must be
2
2
2
. Thus, the other
2
2
2
sides are congruent by Triangle Inequality. Thus, for the perimeter to be
100
100
100
, both of the other sides must be
49
49
49
, but as
49
49
49
is obviously composite, the answer is thus
0
\boxed{0}
0
.
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