The Pedoe's inequality reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Pedoe's inequality

In geometry, Pedoe's inequality states that if a, b, and c are the lengths of the sides of a triangle with area f, and A, B, and C are the lengths of the sides of a triangle with area F, then

with equality if and only if the two triangles are similar.

References

"A Two-Triangle Inequality", D. Pedoe, The American Mathematical Monthly, volume 70, number 9, page 1012, November, 1963.

"An Inequality for Two Triangles", D. Pedoe, Proceedings of the Cambridge Philosophical Society, volume 38, part 4, page 397, 1943.