2011 AIME II Problems/Problem 2
On square ABCD, point E lies on side AD and point F lies on side BC, so that BE=EF=FD=30. Find the area of the square ABCD.
Drawing the square and examining the given lengths, you find that the three segments cut the square into three equal horizontal sections. Therefore, ( being the side length), , or . Solving for , we get , and
Area of the square is