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

Guest Jan 29, 2022

#1**+1 **

What is the largest possible length of the shortest side of the parallelogram?

**Hello Guest!**

The longest side of the parallelogram is when the diagonals are perpendicular to each other. It will be a four-sided rhombus. The length of the sides is

\(s=\sqrt{(\frac{10}{2})^2+(\frac{6}{2})^2}\\ \color{blue}s=5.831\)

!

asinus Jan 29, 2022

#2**+2 **

In radical form, it would be \(\frac{\sqrt{136}}{4}\)

or, \(\frac{2\sqrt{34}}{4}\)or \(\frac{\sqrt{34}}{2}\)

XxmathguyxX Jan 29, 2022