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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 27, 2018
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By the triangle inequality  we have that

 

S  + 33 > 42     where S is the shortest side

 

Subtract 33 from each side

 

S  >  9  units

 

So...since the shortest side has an integer length.....this length must be  10 units

 

So....the least perimeter  is    10  + 33 + 42   =   85 units

 

 

cool cool cool

 Jun 27, 2018

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