help to solve a sequence problem

hi,friends.
There are 99 wood clubs of length 1,2,3,...,99 respectively.Now arrange them in a rectangle (along the a rectangle's 4 sides) with each club's end stick to the other's beginning,but we can't break the clubs.Can we do it? And can we arrange them in a square?If possible,why?
I just get some ideas as follows: can't arrange them in a square! Because (1+2+3+...+99)/4 is not an integer.But I can't prove why they can form a rectangle(the correct answer).
Who can help me?
thanks advancely,
.