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# D is a point on the side AC of a triangle ABC. Is ABC

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Intern
Joined: 29 Jul 2005
Posts: 36
D is a point on the side AC of a triangle ABC. Is ABC [#permalink]

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17 Aug 2005, 12:05
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1. D is a point on the side AC of a triangle ABC. Is ABC isoceles?

1. The area of triangular region ABD = area of BDC.
2. BD perpendicular AC and AD = DC.

2. If the area of triangular region ABC is 25, what is the perimeter of ABC?

1. The length of one side of ABC is 5sqrt(2).
2. RST is a right isoceles triangle.
Manager
Joined: 28 Jun 2005
Posts: 214

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17 Aug 2005, 12:24
Priti wrote:
1. D is a point on the side AC of a triangle ABC. Is ABC isoceles?

1. The area of triangular region ABD = area of BDC.
2. BD perpendicular AC and AD = DC.

2. If the area of triangular region ABC is 25, what is the perimeter of ABC?

1. The length of one side of ABC is 5sqrt(2).
2. RST is a right isoceles triangle.

B & B

Last edited by gotoknow3 on 18 Aug 2005, 05:36, edited 1 time in total.
Intern
Joined: 29 Jul 2005
Posts: 36

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17 Aug 2005, 12:29
Gotoknow3, how did you get base = height for the 2 Q?
Is there any formula that gives the height, area of an isoceles triangle based on its equal sides?
Senior Manager
Joined: 29 Nov 2004
Posts: 483
Location: Chicago

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17 Aug 2005, 12:32
gotoknow3 wrote:
Priti wrote:
1. D is a point on the side AC of a triangle ABC. Is ABC isoceles?

1. The area of triangular region ABD = area of BDC.
2. BD perpendicular AC and AD = DC.

2. If the area of triangular region ABC is 25, what is the perimeter of ABC?

1. The length of one side of ABC is 5sqrt(2).
2. RST is a right isoceles triangle.

1. It can be equilateral or isoceles; E
2. st 1 gives base=height
st 2 gives information on the other side
so C

DO nto agree with inference from condition 1, It can be equilateral or isoceles, IMO there are lot more possiblities

Is equalateral trianlge is isoceles, since two sides are equal?
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Senior Manager
Joined: 30 May 2005
Posts: 373

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17 Aug 2005, 13:43
Priti wrote:
1. D is a point on the side AC of a triangle ABC. Is ABC isoceles?

1. The area of triangular region ABD = area of BDC.
2. BD perpendicular AC and AD = DC.

S1 is insufficient.

S2 is sufficient. This is because Triangles BDC and BDA are both right triangles with BD as the height and DC = DA. 2 equal sides and included angle equal makes them congruent, therefore BA = BC.

Note that all equilateral triangles are isoscles as well. B is my choice.
Senior Manager
Joined: 30 May 2005
Posts: 373

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17 Aug 2005, 13:50
Quote:
2. If the area of triangular region ABC is 25, what is the perimeter of ABC?

1. The length of one side of ABC is 5sqrt(2).
2. RST is a right isoceles triangle.

I think S2 refers to ABC and not RST. Assuming that:

S1 is insufficient.

Consider S2.

Area of a right isoscles triangle is (a^2) /2 where a is the length of each of the equal sides. This is sufficient to calculate all 3 sides - 5 * sqrt(2), 5 * sqrt (2) and 10.

B is my choice.
SVP
Joined: 03 Jan 2005
Posts: 2233

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17 Aug 2005, 19:58
Priti wrote:
1. D is a point on the side AC of a triangle ABC. Is ABC isoceles?

1. The area of triangular region ABD = area of BDC.
2. BD perpendicular AC and AD = DC.

1. Insufficient.
Try draw a graph yourself and you'll know that this will be true if AD=DC, even if when ABC is not isoceles. If BD is perpendicular to AC then ABC is isoceles, otherwise it is not.

2. Sufficient
Triangle ABD and triangle CBD are similar (AD=CD, BD=BD, angle BDA=angle BDC), therefore BA=BC.

B

Quote:
2. If the area of triangular region ABC is 25, what is the perimeter of ABC?

1. The length of one side of ABC is 5sqrt(2).
2. ABC is a right isoceles triangle.

1. Insufficient.
2. Sufficient.
Say angle ABC is 90 degree, then we know that the other two angles are 45 degrees and the three sides are 1:1:sqrt(2). From S=1/2BA*BC=25 and BA=BC we can solve for BA, then the other two sides, and thus the perimeter.

B
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Intern
Joined: 29 Jul 2005
Posts: 36

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18 Aug 2005, 02:39
OAs are

1) B

2) B

Thanks everyone.
Manager
Joined: 07 Oct 2004
Posts: 99

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18 Aug 2005, 11:54
Regarding First question, statement 2, the triangle could be equilateral, thus isosceles is not the only option.

Does isosceles mean exactly 2 equal sides or at least 2 equal sides?
SVP
Joined: 03 Jan 2005
Posts: 2233

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18 Aug 2005, 17:00
The isosceles is a special case of equilateral.
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Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

18 Aug 2005, 17:00
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