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Gmat practice test 1

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by vladmire » Tue Oct 14, 2008 4:56 pm
In the rectangular coordinate system above the area of triangle pqr is what fraction of the area triangle lmn?

1/9
1/8
1/6
1/5
1/3


its a triangle within a triangle with the points L= 2,0 P = 6,0 R = 10,0 N = 14,0 Q = 8,4 M = 8,12

can anyone help me

and if this has already been solved what should I have typed in the search field to find it
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by Gmatss » Tue Oct 14, 2008 5:15 pm
just find the area of 2 triangles.

Pqr=1/2 b.h
1/2 (4)* 4= 8

lmn=1/2 b.h
1/2 (12)* 12)=72

so 8/72= 1/9
A
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by gmat009 » Fri Oct 17, 2008 10:01 am
somehow I am getting ans 1/3.
What's OA
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by mental » Fri Oct 17, 2008 10:21 am
OA is 1/9

it was posted on forum sometime back with the picture.
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by gmat009 » Fri Oct 17, 2008 10:26 am
mental wrote:OA is 1/9

it was posted on forum sometime back with the picture.
I cannot find it. Do you have the link.....
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by mental » Fri Oct 17, 2008 10:37 am
I am unable to look for it

anyway will try to give a brief solution

as you see that points L,P,R,N all lie on x-axis

triangle LMN, base = LN = 12 (difference of x-odinates)
height = y-ordinate of m = 12, as the perpencular distance from x-axis
AREA = 12*12/2=72

Triangle PQR, base = PR = 4 (10-6)
height = 4
AREA = 4*4/2=8

ratio = 8/72 = 1/9


...........................
also if you see, they are similar isoceles triangles

also their bases are in ratio 1:3
also heights in 1:3

so area will be 1:9

.......................................
hope that helps
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by gmat009 » Fri Oct 17, 2008 10:53 am
mental wrote:I am unable to look for it

anyway will try to give a brief solution

as you see that points L,P,R,N all lie on x-axis

triangle LMN, base = LN = 12 (difference of x-odinates)
height = y-ordinate of m = 12, as the perpencular distance from x-axis
AREA = 12*12/2=72

Triangle PQR, base = PR = 4 (10-6)
height = 4
AREA = 4*4/2=8

ratio = 8/72 = 1/9


...........................
also if you see, they are similar isoceles triangles

also their bases are in ratio 1:3
also heights in 1:3

so area will be 1:9

.......................................
hope that helps
Thanks a lot.......
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