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341) Find area of triangle

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341) Find area of triangle

by ern5231 » Tue May 18, 2010 5:45 am
A rectangle ABCD has vertex E(of a triangle) on side AD. The other vertices of triangle, G and F, lie on the edge BC. The area of the rectangle is 24.What is the area of triangle GEF.
1) DC = 4, 2) GF = 1/3BC
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Source: — Data Sufficiency |
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by asamaverick » Tue May 18, 2010 7:12 am
Image
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Given Area = 24.

1) DC = 4.
Since Area = 24, this only tells us that AD = BC = 6.
Not enough to know the area of triangle.
2) GF = 1/3 BC
Not knowing the actual length of at least one side we cannot calculate area of triangle.

Combining both gives. DC = 4. Hence BC = 6. Which gives GF = 2. This is enough to calculate the area of triangle.
Hence answer is C.
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by raviki8208 » Tue May 18, 2010 8:08 am
ern5231 wrote:A rectangle ABCD has vertex E(of a triangle) on side AD. The other vertices of triangle, G and F, lie on the edge BC. The area of the rectangle is 24.What is the area of triangle GEF.
1) DC = 4, 2) GF = 1/3BC

using 1 alone,
Area(GEF) = 1/2 * GF * DC. GF is unknown so unsufficient
using 2 alone
Given GF = 1/3 * BC

Image



Area(GEF) / Area(XYGF) = ((1/2) * GF * DC) / (GF * DC) = 1/2
Area(XYGF) / Area(ABCD) = GF * DC / BC * DC = GF / BC= 1/3
Area(GEF)/Area(ABCD) = 1/6.. sufficient so Answer is B
what is OA?
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by asamaverick » Tue May 18, 2010 9:11 am
raviki8208 wrote:
ern5231 wrote:A rectangle ABCD has vertex E(of a triangle) on side AD. The other vertices of triangle, G and F, lie on the edge BC. The area of the rectangle is 24.What is the area of triangle GEF.
1) DC = 4, 2) GF = 1/3BC

using 1 alone,
Area(GEF) = 1/2 * GF * DC. GF is unknown so unsufficient
using 2 alone
Given GF = 1/3 * BC

Image



Area(GEF) / Area(XYGF) = ((1/2) * GF * DC) / (GF * DC) = 1/2
Area(XYGF) / Area(ABCD) = GF * DC / BC * DC = GF / BC= 1/3
Area(GEF)/Area(ABCD) = 1/6.. sufficient so Answer is B
what is OA?
You are right...it has to be B. I missed that part, drawing the rectangle XYGF makes it so much more clear.
Thanks.
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