Pythagorean Triples

Pythagorean Triples

How to solve the Pythagorean triple problems: commonly used triples, examples, and their solutions.

Triples

Pythagorean Triples are three positive integers that satisfy the Pythagorean theorem. (3, 4, 5), (5, 12, 13), (7, 24, 25)

Pythagorean Triples are three positive integers
that satisfy the Pythagoran theorem: a2 + b2 = c2.

Commonly used triples:
(3, 4, 5)
(5, 12, 13)
(7, 24, 25)

Example 1

Find the value of x. The lengths of the right triangle's legs: 4, x. The length of the right triangle's hypotenuse: 5.

For the right triangle,
the leg is 4,
and the hypotenuse is 5.

Then the related triple is (3, 4, 5).

So x = 3.

Example 2

Find the value of x. The lengths of the right triangle's legs: 5, 12. The length of the right triangle's hypotenuse: x.

For the right triangle,
the legs are 5 and 12.

Then the related triple is (5, 12, 13).

So x = 13.

Example 3

Find the value of x. The lengths of the right triangle's legs: 6, x. The length of the right triangle's hypotenuse: 10.

For the right triangle,
the leg is 6,
and the hypotenuse is 10.

Then the related triple is (3, 4, 5),
because the given triangle
is similar to (3, 4, 5) triangle.

To find the scale (× 2) clearly,
draw the (3, 4, 5) triangle
next to the given triangle.

So x = 2⋅4 = 8.