The sides of a triangle are equal to integral numbers of units. Two of the sides are 4 and 6 units long respectively; what is the minimum value for the triangle's perimeter?
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Any thoughts? Can you, say, list all the cases where the third side is less than or equal to $4$? – lulu Jan 02 '18 at 03:13
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If a,b,and c are the sides of a triangle, how does a+b compare to c? – Steven Alexis Gregory Jan 02 '18 at 03:14
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Look up triangle inequality. – TurlocTheRed Oct 24 '18 at 14:49
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If one side is 4, and other side is 6. Let the third side be c.
Now we are looking for the minimum length, and we know that sum of sides is always larger than the third. (Here 6 is the largest.) So comparing,
$$4+c>6$$
$$c>2$$
Therefore, It's minimum value is 3.
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