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The lengths of two sides of a triangle are 33 units and 42 units. The third side also has an integral length. What is the least possible number of units in the perimeter of the triangle?

 Jun 15, 2019
 #1
avatar+208 
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Hey- Check out this link: https://web2.0calc.com/questions/inequalities-in-triangles

 Jun 15, 2019
 #2
avatar+208 
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Tell me if it helps... :P

NoobGuest  Jun 15, 2019
 #3
avatar+28125 
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Lie the two given lengths on top of each other.  If you join them with a third length of 9 units you will have a straight line, but if you increase the length of the third length by 1 unit while keeping the ends joined you will get a triangle.  Hence shortest third length is 10 units.  I'm sure you can add up the lengths to get the perimeter.

 Jun 16, 2019
 #4
avatar+4322 
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We have the sides x units, 33 units, and 42 units.

 

Thus, we have x>42-33

 

x>9

 

x=10 units.

 

Thus, the smallest possible perimeter will be \(10+33+42=43+42=\boxed{85}\) units.

 Jun 16, 2019

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