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Two diagonals of a parallelogram have lengths 6 and \(10\). What is the largest possible length of the shortest side of the parallelogram?

 Apr 15, 2022
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Disclaimer : not totally sure about this  one  !!!

 

Assuming the  parallelgram  is  not a rhombus  (all sides would be equal)

 

The diagonals will bisect each other   and we can form  a triangle composed of lengths 3 ,5  and the length of the  shortest side, S

 

By the triangle inequality

 

S + 3 > 5                    and           3 + 5  >  S

S > 2                                                8 >  S

 

So......the shortest side must be  < 8 units    but  >  2 units

 

 

cool cool cool

 Apr 15, 2022

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