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Equation x/2 +y/2=5 encloses a certain region on the [#permalink]
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09 Sep 2007, 15:26
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Equation x/2 +y/2=5 encloses a certain region on the coordinate plane..
What is the area of the region?
A 20
B. 50
C. 100
D. 200
E. 400
I read the explanation
I have no idea how we know the above region encloses a square
I am totally lost on this
Can anyone help me out?



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Re: Geometry QuestionNot sure where they got the theory [#permalink]
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09 Sep 2007, 15:44
jamesrwrightiii wrote: Equation x/2 +y/2=5 encloses a certain region on the coordinate plane. What is the area of the region?
A 20 B. 50 C. 100 D. 200 E. 400
I read the explanation I have no idea how we know the above region encloses a square I am totally lost on this Can anyone help me out?
draw xy plane. go for 10 left, right, up and down. then you get a square with a side of 10sqrt2.
so the ares = (10sqrt^2)^2 = 200



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I am still confused though...actually the answer is C
I am still confused how you know it's a square..
If you multiply everything by 2, then you have X + Y=10
Why can't you have numbers such as 6 and 4..or 8 and 2..or 9 and 1?



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jamesrwrightiii wrote: I am still confused though...actually the answer is C
I am still confused how you know it's a square..
If you multiply everything by 2, then you have X + Y=10
Why can't you have numbers such as 6 and 4..or 8 and 2..or 9 and 1?
no fistail is right... it is 200 (choice D)
just draw it into a plan and you notice that it is a square with side of 10*sqrt(2)



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Re: Geometry QuestionNot sure where they got the theory [#permalink]
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09 Sep 2007, 16:17
Fistail wrote: jamesrwrightiii wrote: Equation x/2 +y/2=5 encloses a certain region on the coordinate plane. What is the area of the region?
A 20 B. 50 C. 100 D. 200 E. 400
I read the explanation I have no idea how we know the above region encloses a square I am totally lost on this Can anyone help me out? draw xy plane. go for 10 left, right, up and down. then you get a square with a side of 10sqrt2. so the ares = (10sqrt^2)^2 = 200
Ok here is what I am confused about..
All the equation says is that x+y=10
I am just not sure how we know to go 10 over for each side when all the equation says is that X and Y need to equal 10...?



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Re: Geometry QuestionNot sure where they got the theory [#permalink]
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09 Sep 2007, 16:38
well to be more specific..its the x^2y^2 plane
if x^2=0 then y^2=10
if x^2=10 then y^2=0
now remember this x and y so y^2=10 when x^2=0 etc..
you will realize that the region is a square..and that the side of the square is sqrt(2)10.
area of the square=200
Fistail wrote: jamesrwrightiii wrote: Equation x/2 +y/2=5 encloses a certain region on the coordinate plane. What is the area of the region?
A 20 B. 50 C. 100 D. 200 E. 400
I read the explanation I have no idea how we know the above region encloses a square I am totally lost on this Can anyone help me out? draw xy plane. go for 10 left, right, up and down. then you get a square with a side of 10sqrt2. so the ares = (10sqrt^2)^2 = 200



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Re: Geometry QuestionNot sure where they got the theory [#permalink]
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02 Jun 2008, 19:49
If I consider the following points (5,5), (5,5), (5,5) and (5,5), the figure enclosed is a square with an area of 100 sq units.
Should the question be what is the max area of the region?
Thanks.



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Re: Geometry QuestionNot sure where they got the theory [#permalink]
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03 Jun 2008, 03:45
I agree with rakesh22.It should be a square of each side 10. so area is 100 i.e. C rakesh22 wrote: If I consider the following points (5,5), (5,5), (5,5) and (5,5), the figure enclosed is a square with an area of 100 sq units.
Should the question be what is the max area of the region?
Thanks.



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Re: Geometry QuestionNot sure where they got the theory [#permalink]
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03 Jun 2008, 07:34
you know what i agree with 100..cause we only focus on half of the square...
walker..what do u think?



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Re: Geometry QuestionNot sure where they got the theory [#permalink]
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03 Jun 2008, 07:40
Look at the first quadrant (x >0, y > 0) : x + y = 10, so we get a line segment with endpoints (0,10) and (10,0). We will get a square that can be broken up into 4 right triangles, each with area (10)(10)/2 = 50



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Re: Geometry QuestionNot sure where they got the theory [#permalink]
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03 Jun 2008, 07:42
kevincan wrote: Look at the first quadrant (x >0, y > 0) : x + y = 10, so we get a line segment with endpoints (0,10) and (10,0). We will get a square that can be broken up into 4 right triangles, each with area (10)(10)/2 = 50 but arent we only looking for the triangles in region 1 and 2?



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Re: Geometry QuestionNot sure where they got the theory [#permalink]
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03 Jun 2008, 07:49
never mind..
i got confused by the other posters..grrrrrrr
this is 200..
x+y=10
condition1 x>0 y>0
x+y=10...you get a triangle with slope 10sqrt(2)
condition 2 x<0 y<0
xy=10 y=10+x..
condition 3 x>0 y<0 xy=10 y=10x
and condition 4 x<0 y>0 x+y=10 y=10+x



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Re: Geometry QuestionNot sure where they got the theory [#permalink]
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03 Jun 2008, 08:07
fresinha12 wrote: never mind..
i got confused by the other posters..grrrrrrr
this is 200..
x+y=10
condition1 x>0 y>0
x+y=10...you get a triangle with slope 10sqrt(2)
condition 2 x<0 y<0
xy=10 y=10+x..
condition 3 x>0 y<0 xy=10 y=10x
and condition 4 x<0 y>0 x+y=10 y=10+x I really dont see how ur getting sides of 10sqrt2. You plug in for x or y in the original and you get 5,5,5,5 etc... This is square w/ sides of 10. What am I missing here?



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Re: Geometry QuestionNot sure where they got the theory [#permalink]
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03 Jun 2008, 08:12
GMATBLACKBELT wrote: fresinha12 wrote: I really dont see how ur getting sides of 10sqrt2. You plug in for x or y in the original and you get 5,5,5,5 etc... This is square w/ sides of 10. What am I missing here? ok lets see.. x/2+y/2=5 => x+y=10 suppose x=0 and y is positive..y/2=5 y=10.. get it? the question is asking about the area occupied by the region given by the equation x+y=10.. the x/2+y/2 is just to throw you off..the actual equation is x+y=10




Re: Geometry QuestionNot sure where they got the theory
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