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Area of a triangle

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by GMATGuruNY » Thu Apr 03, 2014 5:08 am
In the rectangular coordinate system below, the are of triangular region PQR is

12.5
14
10srt2
16
25
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The area of the rectangle drawn around triangle PQR = 7*4 = 28.
Since triangle PQR takes up less than half the rectangle, PQR < 14.

The correct answer is A.

To understand why PQR must take up less than half the rectangle, check my second post here:
https://www.beatthegmat.com/area-of-pqr-t115199.html
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by Jim@StratusPrep » Thu Apr 03, 2014 5:11 am
The base and the height must be perpendicular, so this cannot be the case. If you draw a rectangle around the triangle, starting at the origin to point (7,4) you will get and area of 28. Then you can subtract the 'negative space' around the inner triangle. This is easy to do as all of the spaces are right triangles.

Total area = 28

Lower right triangle = .5(3)(4) = 6
Lower left triangle = .5(4)(3) = 6
Upper left triangle = (.5)(1)(7) = 3.5

28 - 15.5 = 12.5

A
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by Brent@GMATPrepNow » Thu Apr 03, 2014 7:00 am
Here's a drawing that illustrates Jim's solution:
Image

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