What’s the area of the triangle in terms of P?

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umaa: Legendary Member; Posts: 727; Joined: Sun Jun 08, 2008 9:32 pmFollowed by: 1 member; Thanked: 8 times

by umaa » Mon Jul 21, 2008 6:31 am

P is the perimeter of an equilateral triangle. What’s the area of the triangle in terms of P?

1. (P ^ 2)(sqrt3)/72

2. (P ^ 2)/3

3. (P ^ 2)/6

4. P(sqrt3)/54

5. (P ^ 2)(sqrt3)/6

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Source: Beat The GMAT — Problem Solving | Mon Jul 21, 2008 6:31 am

reachac: Legendary Member; Posts: 572; Joined: Fri Feb 22, 2008 9:25 am; Thanked: 21 times

by reachac » Mon Jul 21, 2008 6:35 am

Are the options correct?

I got an ans (P ^ 2)(sqrt3)/36

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umaa: Legendary Member; Posts: 727; Joined: Sun Jun 08, 2008 9:32 pmFollowed by: 1 member; Thanked: 8 times

by umaa » Mon Jul 21, 2008 6:39 am

Hey,
Right. even i got the same answer.

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VP_Tatiana: GMAT Instructor; Posts: 189; Joined: Thu May 01, 2008 10:55 pmFollowed by: 1 member; Location: Seattle, WA; Thanked: 25 times; GMAT Score:750+

by VP_Tatiana » Mon Jul 21, 2008 6:43 am

I also got what reachac got.

Draw a vertical line dividing the triangle in half. Now, 1/2 of the base is P/6. To find the height, look at one of the two 30-60-90 triangles you created. Remembering the proportion for this type of triangle tells you that the side opposite the 60 degree angle (the height) is sqrt3 times the side opposite the 30 degree angle, p/6. So, we have a height of P*sqrt3/6.

1/2 bh = (p/6)*(psqrt3/6) = (p^2)sqrt3/36

Tatiana Becker | GMAT Instructor | Veritas Prep

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Mon Jul 21, 2008 9:12 am

Even i got P^2/(12sqrt 3)

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parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

by parallel_chase » Mon Jul 21, 2008 1:47 pm

There is definitely something wrong with the answer choices or the question.

Even i got the same answer P^2/12sqrt3 or P^2sqrt3/36

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