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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
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+2

reposted for readability

 

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

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 Aug 19, 2019
 #2
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+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

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