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# equation

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Manager
Joined: 21 Feb 2010
Posts: 214
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Kudos [?]: 13 [0], given: 1

equation [#permalink]  03 Sep 2010, 13:45
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
If equation l x/2l + ly/2l + 5 encloses a certain region on the coordinate plane, what is the area of this region?

(C) 2008 GMAT Club - m25#19

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how do we know this is an equation of a square?
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Math Expert
Joined: 02 Sep 2009
Posts: 23049
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Kudos [?]: 27180 [0], given: 2724

Re: equation [#permalink]  03 Sep 2010, 14:18
Expert's post
|\frac{x}{2}| + |\frac{y}{2}| = 5

You will have 4 case:

x<0 and y<0 --> -\frac{x}{2}-\frac{y}{2}=5 --> y=-10-x;

x<0 and y\geq{0} --> -\frac{x}{2}+\frac{y}{2}=5 --> y=10+x;

x\geq{0} and y<0 --> \frac{x}{2}-\frac{y}{2}=5 --> y=x-10;

x\geq{0} and y\geq{0} --> \frac{x}{2}+\frac{y}{2}=5 --> y=10-x;

So we have equations of 4 lines. If you draw these four lines you'll see that the figure which is bounded by them is square which is turned by 90 degrees and has a center at the origin. This square will have a diagonal equal to 20, so the Area_{square}=\frac{d^2}{2}=\frac{20*20}{2}=200.

Or the Side= \sqrt{200} --> area=side^2=200.

Similar problem: graphs-modulus-help-86549.html?hilit=horizontal#p649401

Hope it's clear.
_________________
Re: equation   [#permalink] 03 Sep 2010, 14:18
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