The method of finding the extreme value by column function can prove that:

Let BC=a as the base, H as the height, D as the intersection of the high line and the base, and BD=x as the x,

The waist length of the triangle is set to m and n,

Do you have an m? =h？ +x？ ，n？ =h？ +(a-x)？

Circumference y=m+n+a=√(h? +x？ )+√[h？ +(a-x)？ ]+a

Right y=√(h? +x？ )+√[h？ +(a-x)？ ]+a derivative

y'=[x/√(h？ +x？ )]-[(a-x)/√[h？ +(a-x)？ ]

Can stagnation get x? h？ -(a-x)h？ =0, which means x? =(a-x)？

X = (a-x), let x=a-x, a=2x,

That is BC=2*BD, which proves that the circumference of point D is the smallest when it is at the midpoint of the bottom.

At this point, the triangle is isosceles.