Pythagorean Triple

A Pythagorean triple, commonly written as

(a, b, c),

is a set of three natural numbers that satisfy the Pythagorean Theorem.

a^{2} + b^{2} = c^{2}

A right triangle can be drawn using the numbers of a Pythagorean triple as its side lengths. The lowest valued set of numbers that form a Pythagorean triple are

3,

4,

and

5 .

There are infinitely many Pythagorean triples. The following table shows a few.

Triple	Substitute in $a^{2} + b^{2} = c^{2}$	Simplify
$(3, 4, 5)$	$3^{2} + 4^{2} = ? 5^{2}$	$9 + 16 = 25 ✓$
$(5, 12, 13)$	$5^{2} + 12^{2} = ? 13^{2}$	$25 + 144 = 169 ✓$
$(8, 15, 17)$	$8^{2} + 15^{2} = ? 17^{2}$	$64 + 225 = 289 ✓$
$(7, 24, 25)$	$7^{2} + 24^{2} = ? 25^{2}$	$49 + 576 = 625 ✓$

If $(a, b, c)$ is a Pythagorean triple, then so is $(k a, k b, k c)$ for any natural number $k .$

$(a, b, c)$	$k$	$(k a, k b, k c)$
$(3, 4, 5)$	$3$	$(3 (3), 3 (4), 3 (5))$ $⇕$ $(9, 12, 15)$
$(5, 12, 13)$	$2$	$(2 (5), 2 (12), 2 (13))$ $⇕$ $(10, 24, 26)$

	{{ 'ml-lesson-number-slides' \| message : article.intro.bblockCount }}
	{{ 'ml-lesson-number-exercises' \| message : article.intro.exerciseCount }}
	{{ 'ml-lesson-time-estimation' \| message }}

{{ article.displayTitle }}