MathDB

B6

Part of 1982 Putnam

Problems(1)

the area of triangles

Source:

6/19/2011
Denote by S(a,b,c)S(a,b,c) the area of a triangle whose lengthes of three sides are a,b,ca,b,c Prove that for any positive real numbers a1,b1,c1a_{1},b_{1},c_{1} and a2,b2,c2a_{2},b_{2},c_{2} which can serve as the lengthes of three sides of two triangles respectively ,we have S(a1,b1,c1)+S(a2,b2,c2)≤S(a1+a2,b1+b2,c1+c2) \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})}
geometryinequalitiesarea of a triangleHeron's formulainequalities unsolved