2011 AIME II Problems/Problem 2

Problem:

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.

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Solution:

Drawing the square and examining the given lengths, you find that the three segments cut the square into three equal horizontal sections (I dont know how to make a diagram so somebody please insert one) Therefore, (x being the side length), , or . SOlving for x, we get that x=9sqrt(10), and x^2=810

Area of the square is 810.