Question

If you solve this you are officially amazing!
"The diagonals of a trapezoid are perpendicular and have lengths 8 and 10. Find the length of the median of the trapezoid."

Answer 1

I don't think this is determined. Take a look at

http://mathcentral.uregina.ca/QQ/database/QQ.09.07/h/amanda1.html

and you can see that depending on how you divide the diagonals, the median can be a variety of lengths.