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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