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existence of triangle with sides √a,√b,√c

Source: Serbia 2003 2nd Grade P1

May 13, 2021

geometryTriangle

Problem Statement

Given a

\triangle ABC

with the edges

a,b

and

c

and the area

S

:
(a) Prove that there exists

\triangle A_1B_1C_1

with the sides

\sqrt a,\sqrt b

and

\sqrt c

. (b) If

S_1

is the area of

\triangle A_1B_1C_1

, prove that

S_1^2\ge\frac{S\sqrt3}4

.

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