Question

which of the following are pythagorean triples? select all that apply.
show your work here
(12,16,20)
(9,12,15)
(8,15,17)
(4,7,9)
(3,4,5)

Explanation:

Step1: Recall Pythagorean theorem

A triple $(a,b,c)$ satisfies $a^2 + b^2 = c^2$, where $c$ is the largest number.

Step2: Test (12,16,20)

Calculate squares and sum:
$12^2 + 16^2 = 144 + 256 = 400$
$20^2 = 400$
$12^2 + 16^2 = 20^2$

Step3: Test (9,12,15)

Calculate squares and sum:
$9^2 + 12^2 = 81 + 144 = 225$
$15^2 = 225$
$9^2 + 12^2 = 15^2$

Step4: Test (8,15,17)

Calculate squares and sum:
$8^2 + 15^2 = 64 + 225 = 289$
$17^2 = 289$
$8^2 + 15^2 = 17^2$

Step5: Test (4,7,9)

Calculate squares and sum:
$4^2 + 7^2 = 16 + 49 = 65$
$9^2 = 81$
$4^2 + 7^2
eq 9^2$

Step6: Test (3,4,5)

Calculate squares and sum:
$3^2 + 4^2 = 9 + 16 = 25$
$5^2 = 25$
$3^2 + 4^2 = 5^2$

Answer:

(12, 16, 20), (9, 12, 15), (8, 15, 17), (3, 4, 5)