Tiling right triangles
Geometry
Level
5
As shown above, I've put together 4 right-triangled tiles with all integer side lengths, to form a quadrilateral.
What is the smallest possible perimeter of this quadrilateral if it has all distinct sides?
The answer is 176.
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1 solution
Just going through pythagorean triples up to first 75, we get,
15-20-25; 20-48-52; 36-48-60; 36-15-39, where there are four pairs of legs, each pair having equal side lengths.
These legs are four parts of two diagonals, that cross at right angles.
There hypotenuse add up to 1 7 6 .