The side lengths of a triangle are consecutive integers.
The largest interior angle is twice the smallest.

What are the side lengths of the triangle?

Hi!

Let be our triangle ABC.

Let be A the smalest angle and B = 2*A and so C = PI - 3*A.

Let be BM the bisector of the B angle.

The triangle AMB has same angles with the triangle ABC so from Thales

BM/(x+1) = MC/x = x/(x+2) 

So BM = x*(x+1)/(x+2)

and MC = x^2/(x+2)

But AM = AC - MC = (x+2) - x^2/(x+2) = 4*(x+1) / (x+2)

But the triangle ABM has 2 egual abgles so AM = BM so

x*(x+1)/(x+2) = 4*(x+1)/(x+2) so x=4

So the side lengts are 4,5,6

Have a nice day!

 

Posted by Chesca Ciprian on 2009-03-06 06:03:19