In this question in my textbook:
Let $A(0,1), B(1,1), C(1,-1), D(-1,0)$ be four points. If P be any other point, then $PA+PB+PC+PD=d$, where $[d] =$
What I have done: Taken two triangles $PAB$ and $PAD$, we know that the sum of two sides is greater than the other, thus $PA+PB≥AB$ and $PC+PD≥CD$, adding we get: $PA+PB+PC+PD≥AB+CD$. This approach gives $3$, and if we take the triangles $PAC$ and $PCD$, we get $4$, which is the correct one. Why this discrepancy?