Pythagorean Triple Calculator

Find All Triangles with a Given Perimeter


Pythagorean Triple Calculator

Enter the perimeter of the right triangle:

 

If a right triangle has legs of length A and B and a hypotenuse of length C, then the relation among A, B, and C is

A2 + B2 = C2, or
sqrt(A2 + B2) = C

When A, B, and C are integers, the set (A, B, C) is called a Pythagorean Triple. Some basic examples of Pythagorean Triples are

(3, 4, 5)
(5, 12, 13)
(8, 15, 17)
(7, 24, 25)
(20, 21, 29)

These examples are called primitive because none of the three numbers in each set share common factors. The set (10, 24, 26) is another Pythagorean Triple, but it is not primitive because you can divide each element by 2, yielding the primitive set (5, 12, 13). Every non-primitive set can be reduced to a primitive set.

There are many Pythagorean triangles that have the same perimeter, that is, A + B + C is constant for each triangle in the group. For example, there are five Pythagorean right triangles that have a perimeter of 1200:

(48, 575, 577)
(75, 560, 565)
(200, 480, 520)
(240, 450, 510)
(300, 400, 500)

The smallest number for which there are five Pythagorean triangles with that perimeter is 420:

(28, 195, 197)
(60, 175, 185)
(70, 168, 182)
(105, 140, 175)
(120, 126, 174)

You can use the Pythagorean Triple Calculator above to find all the integer right triangles that have a given perimeter.


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