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DS on triangles

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DS on triangles

by satishchandra » Tue Nov 22, 2011 9:21 pm
Is area of triangle DEF greater than area of triangle ABC ?

1. The value of area of triangle DEF is less than that of perimeter of traingle ABC.
2. Angles of triangle DEF = Angles of traingle ABC.
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Source: — Data Sufficiency |
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by shankar.ashwin » Tue Nov 22, 2011 10:45 pm
E IMO.
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by fcabanski » Wed Nov 23, 2011 1:07 am
E.

1 Insufficient. DEF could be identical to ABC yet still have an area smaller than ABC's perimeter. DEF could have a larger area, or smaller than ABC's perimeter yet still have a larger or smaller area.

2. Insufficient. Two triangles can have the same shape and thus the same angles, but different side lengths. For example a 3,4,5 triangle could have sides 3,4,5 or 30,40,50.

Both together. Insufficient. DEF could be a 3,4,5 (area 6) and ABC could be 30,40,50. DEF's area is smaller than ABC's perimeter, while DEF's area is also smaller. Or ABC could be 2,2.6666..., 3.33333333... (3,4,5 with all divided by 1.5, thus all the same angles.) Now DEF's area < ABC's perimeter, but DEF's area > ABC's area.
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by GmatMathPro » Sat Nov 26, 2011 8:55 am
satishchandra wrote:Is area of triangle DEF greater than area of triangle ABC ?

1. The value of area of triangle DEF is less than that of perimeter of traingle ABC.
2. Angles of triangle DEF = Angles of traingle ABC.
Statement 1: Start with something easy, like making DEF a 3-4-5 right triangle. The area is 6. If ABC is also a 3-4-5 right triangle, then its perimeter is 12. So, the area of DEF is less than the perimeter of ABC and the areas are equal. However, if DEF is a 3-4-5 right triangle and ABC is a 6-8-10 right triangle, ABC still has a larger perimeter, but now clearly has a larger area. INSUFFICIENT.

Statement 2: This says the triangles are similar. But clearly either one could be bigger, in terms of area. INSUFFICIENT.

Statements 1&2. The two cases considered in statement 1 are enough to prove this insufficient as well, as all of the triangles were similar. INSUFFICIENT.
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