What is the area of the triangle ABC? : GMAT Data Sufficiency (DS)
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# What is the area of the triangle ABC?

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Joined: 24 Jul 2012
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What is the area of the triangle ABC? [#permalink]

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26 Jul 2012, 04:37
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What is the area of the triangle ABC?

(1) The triangle is inscribed in a semicircle with its diameter as one side of the triangle.The radius of the Semicircle is 10

(2) The triangle is an isosceles triangle.
[Reveal] Spoiler: OA
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Re: What is the area of the triangle ABC? [#permalink]

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26 Jul 2012, 05:02
Statement 1: Inscribed in a semicircle means the angle facing opposite the diameter is 90 degree. Area = 1/2*b*h. b =20. h or height we don't know. h will be different if the triangle is 90-45-45, or 90-30-60. Hence Insufficient
Statement 2: Says its isosceles, but no other detail. no angles, no base or height data. Hence Insufficient.

together we know the triangle is 90-45-45, with base 20. Hence area can be calculated. Sufficient. Ans is C
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Intern
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Kudos [?]: 36 [0], given: 7

Re: What is the area of the triangle ABC? [#permalink]

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26 Jul 2012, 05:48
summer101 wrote:
Statement 1: Inscribed in a semicircle means the angle facing opposite the diameter is 90 degree. Area = 1/2*b*h. b =20. h or height we don't know. h will be different if the triangle is 90-45-45, or 90-30-60. Hence Insufficient
Statement 2: Says its isosceles, but no other detail. no angles, no base or height data. Hence Insufficient.

together we know the triangle is 90-45-45, with base 20. Hence area can be calculated. Sufficient. Ans is C

The angle opposite to the Diameter(i.e., hypotenuse) is 90, so if we draw a line from the mid point of the diameter(point will be center of the circle) to the vertex that is making 90 degrees then it becomes the height(altitude).

So we can calculate the area of the traingle by (1/2)*height*hypotenuse.

So A is sufficient to calculate and i ended up here.

Please correct me if i am missing something here. thanks.
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Re: What is the area of the triangle ABC? [#permalink]

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26 Jul 2012, 06:49
Consider a triangle which is shown here: http://www.flickr.com/photos/janmr/6163380121/
Here height will not be line from the center to vertex.
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Re: What is the area of the triangle ABC? [#permalink]

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26 Aug 2016, 07:05
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Re: What is the area of the triangle ABC?   [#permalink] 26 Aug 2016, 07:05
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