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Minimum perimeter length (Posted on 2010-12-10) Difficulty: 2 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Solution d2 way ?? Comment 5 of 5 |

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. 


  Posted by Ady TZIDON on 2010-12-11 03:42:42
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