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The perimeter of the triangle below is an integer.  What is the smallest possible value of the perimeter?  (Assume that the triangle is non-degenerate.)

 

 Feb 27, 2024
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Let's let the final length of the triangle be equal to x. By the Triangle inequality, 

 

24+49>x

24+x>49

49+x>24.

 

The first inequality gives us the equation x<73. The second equation gives up x>25. The final equation gives up x>-25. From these equations, we know that 25 <73. So the smallest possible length of x is 26. So the perimeter of the triangle is 26+24+49=99. 

 

And now we're done! smiley Hope this helped!

 Feb 27, 2024

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