Drawing triangles around triangle
The right triangle in red has integer side lengths 13-84-85.
Now, I draw in 3 more right triangles such that the hypotenuse of each of these 3 triangles is a side of the red triangle.
Is it possible that the legs of these 3 triangles are all integers?
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1 solution
84 = 4 * 3 * 7 cannot be written as the sum of two squares since its prime decomposition has a prime = 3 mod 4, raised to an odd power. It's also low enough to check by inspection, especially if you look for the primitive pythagorean triple in which the hypotenuse must be odd; and so 7, 3 or 21. No such triple exists.