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0
106
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$$\text{Square A and Square B are both 2009 by 2009 squares. Square A has both its length and width increased by an amount x, while Square B has its length and width decreased by the same amount x. What is the minimum value of x such that the difference in area between the two new squares is at least as great as the area of a 2009 by 2009 square? }$$

Aug 19, 2019

#1
+6045
+2

$$\text{Square A and Square B are both 2009 by 2009 squares.\\ Square A has both its length and width increased by an amount x,\\ while Square B has its length and width decreased by the same amount x.\\~\\ What is the minimum value of x such that the difference in area between\\ the two new squares is at least as great as the area of a 2009 by 2009 square? }$$

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Aug 19, 2019
#2
+1

Thanks Rom: Here is my attempt at this:

(x + 2009)^2 - (2009 - x)^2 = 2009^2

Expand out terms of the left hand side:
8036 x = 4036081

Divide both sides by 8036:
x = 2009/4 = 502.25

Aug 19, 2019