We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
106
2
avatar

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

 Aug 19, 2019
 #1
avatar+6045 
+2

reposted for readability

 

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

.
 Aug 19, 2019
 #2
avatar
+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

29 Online Users