isosceles triangle

[grandh01]

Two of the sides of an isosceles triangle
measure 6 and 6 square root 3, what is its
perimeter?

1) One of the angles of the triangle is obtuse.
2) The perimeter of the triangle is less than 24.

OA IS D

[Anurag@Gurome]

From given we can say that the sides of triangle can be:
6, 6, 6 square root 3
or
6 square root 3, 6 square root 3, 6

consider option 1:
one of the angles is obtuse. so it is not our equal angles, as there cannot be two obtuse angles in a triangle. the side opposite to the larger angle is the largest side. so the largest side is 6 square root 3. so the equal sides are 6.
hence it can be answered with A alone.

consider option 2:
the perimeter of the triangle is less than 24.
only this 6, 6, 6 square root 3 option satisfies.

Hence, it is D

[everything's eventual]

Two sides of the triangle are 6 and 6 square root 3.

So the third side 6 or 6 square root 3

1) One of the angles of the triangle is obtuse.

One angle is obtuse and the two other angles are acute. Sides opposite to the acute angles are equal and smaller than the third side. Therefore the third side is 6.

2) The perimeter of the triangle is less than 24.

Let the third side be 6 square root 3

Therefore, perimter = 6 + 6 square root 3 + 6 square root 3 = apprx 27

But the perimeter is less than 24. Therefore the third side has to be 6.

Therefore perimter = 6 +6 +6 square root 3 = apprx 22.4.

Answer = D