# Equiarea and equiperimeter cut.
Consider a triangle $T$, can we find a line $L$ such that $L$ cuts $T$ into two pieces with the same area and same perimeter?
begin-picture
width="150"; height="100"; border=25
xmin=-1; xmax=3.5; ymin=0; noaxes(); nobutton();
a = [0,0]
b = [4,0]
c = [1,3]
line(a,b)
line(b,c)
line(a,c)
p = [-1,1.5]
q = [4.5,0.5]
line(p,q)
text(p,"L?",above)
end-picture