Question

Two diagonals of a parallelogram have lengths 6 and 8. What is the largest possible length of the shortest side of the parallelogram?

Answer 1

• 5 units

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The intersecting diagonals form a triangle with sides 3, 4 and shorter side x of the parallelogram.

Possible angle measure between diagonals, opposite to shorter side is maximum 90°.

Find the largest possible length of x using the law of cosines:

• 
  `x=√(3^3+4^2-3*4*cos\ 90) =√(25)=5\ units`