The length of each of the sides of a triangle ABC is a positive integer with: ∠ BAC = 2* ∠ ABC and, ∠ ACB is obtuse.

Find the minimum length of the perimeter.

answer:77

I decided to post my solution only after reading others, only to justify the D2 RANKING.

Let us call BD a height from the point B to the base AC.

BD=BC*sin2x

BD=AB*sinx

cosx=AB/(2*BC) has to be rational ,fractional and over .86

the immediate choice being .875 i.e. 7/8

The sequel is like Jer's , and gets you the "two lucky sevens"' result, however precluding few trigo formulas and thus perhaps justifying D2.