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MATH / Square A and Square B are both 2009 by 2009 squares. Square A has both its length and width increased by an amount x, while Square B has its length and width decreased by the same …

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problem

Square A and Square B are both 20092009 by 20092009 squares. Square A has both its length and width increased by an amount xx, while Square B has its length and width decreased by the same amount xx. What is the minimum value of xx such that the difference in area between the two new squares is at least as great as the area of a 20092009 by 20092009 square?
Plain-text mathematical notation (without MathML)
Square A and Square B are both 2009 by 2009 squares.  Square A has both its length and width increased by an amount x, while Square B has its length and width decreased by the same amount x.  What is the minimum value of x such that the difference in area between the two new squares is at least as great as the area of a 2009 by 2009 square?
Original LaTeX notation
Square A and Square B are both $2009$ by $2009$ squares.  Square A has both its length and width increased by an amount $x$, while Square B has its length and width decreased by the same amount $x$.  What is the minimum value of $x$ such that the difference in area between the two new squares is at least as great as the area of a $2009$ by $2009$ square?

level

Level 5

type

Algebra

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