Question

find pythagorean triples
pythagorean triples are sets of three positive, whole numbers that represent the lengths of the sides of a right triangle.
they satisfy the equation $a^2 + b^2 = c^2$, where $a$, $b$, and $c$ are side lengths, with $c$ being the longest side. explore
pythagorean triples by completing each question in this activity.
question 1

determine if each set of numbers represents a pythagorean triple.
select the correct text in the table.

$a$	$b$	$c$	pythagorean triple?
12	35	$20\sqrt{3}$	yes no
5	10	$5\sqrt{5}$	yes no
8	12	15	yes no
20	99	101	yes no

Explanation:

Step1: Check first set (5,12,13)

Calculate $a^2 + b^2$ and $c^2$:
$5^2 + 12^2 = 25 + 144 = 169$
$13^2 = 169$
Since $5^2 + 12^2 = 13^2$, all are whole numbers.

Step2: Check second set (12,35,$20\sqrt{3}$)

$20\sqrt{3}$ is not a whole number, so it fails the definition.

Step3: Check third set (5,10,$5\sqrt{5}$)

$5\sqrt{5}$ is not a whole number, so it fails the definition.

Step4: Check fourth set (8,12,15)

Calculate $a^2 + b^2$ and $c^2$:
$8^2 + 12^2 = 64 + 144 = 208$
$15^2 = 225$
Since $208
eq 225$, it is not a triple.

Step5: Check fifth set (20,99,101)

Calculate $a^2 + b^2$ and $c^2$:
$20^2 + 99^2 = 400 + 9801 = 10201$
$101^2 = 10201$
Since $20^2 + 99^2 = 101^2$, all are whole numbers.

Answer:

a	b	c	Pythagorean triple?
12	35	$20\sqrt{3}$	No
5	10	$5\sqrt{5}$	No
8	12	15	No
20	99	101	Yes