The author of this paper solves an unsolved problem proposed by \textit{H. Steinhaus} [One hundred problems in elementary mathematics, Pergamon, Oxford (1964; Zbl 0116.241), p. 98], that asks for a necessary and sufficient condition on the sides \(p, q, r\) of a triangle \(PQR\) and the sides \(a, b, c\) of a triangle \(ABC\) in order that the area enclosed by \(ABC\) contains a congruent copy of \(PQR\). With \(F\) and \(F'\) the areas of the triangles \(ABC\) and \(PQR\) respectively, the condition is: At least one of the 18 inequalities, obtained by cyclic permutations of \(\{a,b,c\}\) and arbitrary permutations of \(\{p,q,r\}\) in the formula \[ \max\{F(q^ 2 + r^ 2 - p^ 2), F'(b^ 2 + c^ 2 - a^ 2)\} + \max\{F(p^ 2 + r^ 2 - q^ 2), F'(a^ 2 + c^ 2 - b^ 2)\} \leq 2Fcr \] is satisfied.