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