cute_smiley wrote:

i think that (1) insuf

but for the second it cannot be concluded that two angles of the triangle are equal. It can be that y=z+x (all angles are different) from this we can conclude that x+y+z = 180 i.e. y+y=180, y=90 so there is right triangle. But this is not enough because either side can have 90degrees angle so we need first statement: 12^2+15^=k^2, or 15^-12^2=k^2 and so on untill we will get the perimeter which will be the multiple of nine.

Am i right?

I agree with you smiley - we cannot conclude that the two angels are the same but we do still need the first statement so I'm getting answer as C. However, when working through the problem I cant seem to get a suitable numerical answer.

We know that there is an angle of 90 degrees so if the triangle were an isosceles triangle then the sides would have to be in the ratio x: x: x*(sqrt2) which would not allow for sides of 12 and 15 or a perimeter with a multiple of 9.

From 1) we know the perimeter is a multiple of 9. The only configuration of sides with a 90 degree internal angle that would allow this is for the sides to be in the ratio 3:4:5 or 9:12:15 - giving a perimeter of 36.

C is the answer

I understood till the part that says one of the angles is 90. But why cant the other two angles be (35, 55) or (50, 40) .. as they still sum to 90 but not necessarily a special triangle . Please let me know if i am missing something.