Pythagorean Triangles with the Same Area

Explore Pythagorean triangles with the same area. They appear in sets of three because the legs (a and b) and the hypotenuse (c) can be written in three different ways in terms of parameters r and s.

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DETAILS

The lengths of the legs a and b and the hypotenuse c can be written in terms of integers m and n as

(m^2)-(n^2), 2 m n, (m^2)+(n^2)

that have three sets of solutions for m and n given by

(r^2)+r s+(s^2), (r^2)-(s^2);

(r^2)+r s+(s^2), 2 r s+(s^2);

(r^2)+2 r s, (r^2)+r s+(s^2).

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Contributed by: Enrique Zeleny

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