Minimum Value of Triangle

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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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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.