5

Part of 2003 India National Olympiad

Problems(1)

Area is at least .....

Source: India National Olympiad 2003, Problem 5

Let a, b, c be the sidelengths and S the area of a triangle ABC. Denote

x=a+\frac{b}{2}

y=b+\frac{c}{2}

z=c+\frac{a}{2}

. Prove that there exists a triangle with sidelengths x, y, z, and the area of this triangle is

\geq\frac94 S

geometryarea of a triangleHeron's formulageometry solved