Question

which of the following are pythagorean triples? select all that apply.
show your work here
(3,4,5)
(6,8,10)
(9,12,15)
(12,16,20)
(3,7,8)

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Test (3,4,5)

$3^2 + 4^2 = 9 + 16 = 25$, $5^2 = 25$. $25=25$, so valid.

Step3: Test (6,8,10)

$6^2 + 8^2 = 36 + 64 = 100$, $10^2 = 100$. $100=100$, so valid.

Step4: Test (9,12,15)

$9^2 + 12^2 = 81 + 144 = 225$, $15^2 = 225$. $225=225$, so valid.

Step5: Test (12,16,20)

$12^2 + 16^2 = 144 + 256 = 400$, $20^2 = 400$. $400=400$, so valid.

Step6: Test (3,7,8)

$3^2 + 7^2 = 9 + 49 = 58$, $8^2 = 64$. $58
eq64$, so invalid.

Answer:

(3,4,5), (6,8,10), (9,12,15), (12,16,20)