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.

Solution: (Needs better solution, I cannot remember exactly how I got the side length)

Drawing the square and examining the given lengths, you find that the three segments cut the square into three equal horizontal sections (see diagram) Therefore, (x being the side length), $sqrt(x^2+(x/3)^2)=30$ , or $x^2+(x/3)^2=900$ . Solving for x, we get that x=9sqrt(10), and $x^2$ =810

Area of the square is 810.

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2011 AIME II Problems/Problem 2