IBM Ponder This #070 · February 2004

This month's puzzle is from Denis Boris.

Let ABC be a primitive right triangle with integer sides and integer area. ("Primitive" means that the sides are relatively prime.)

Let DEF be an isosceles triangle with integer sides.

Suppose ABC and DEF have the same perimeter, and the same area.

Part 1
Find the lengths of the sides of ABC and of DEF.

Part 2
Prove your solution is unique.
(We do not know the solution to Part 2.)

Solution

Best opened after a real attempt

To be added.