MathDB

Denote by

S(a,b,c)

the area of a triangle whose lengthes of three sides are

a,b,c

Prove that for any positive real numbers

a_{1},b_{1},c_{1}

and

a_{2},b_{2},c_{2}

which can serve as the lengthes of three sides of two triangles respectively ,we have

\sqrt{S(a_{1},b_{1},c_{1})}+\sqrt{S(a_{2},b_{2},c_{2})}\le\sqrt{S(a_{1}+a_{2},b_{1}+b_{2},c_{1}+c_{2})}

Problem Statement