ILL 1978 Problem 8

For two given triangles $A_1A_2A_3$ and $B_1B_2B_3$ with areas $\Delta_A$ and $\Delta_B$ , respectively, $A_iA_k \ge B_iB_k, i, k = 1, 2, 3$ . Prove that $\Delta_A \ge \Delta_B$ if the triangle $A_1A_2A_3$ is not obtuse-angled.