Question

select all the correct answers. which triples are pythagorean triples? (8,15,17) (1,√3,2) (9,12,16) (8,11,14) (20,21,29) (30,40,50)

Explanation:

Step1: Recall Pythagorean triple rule

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

Step2: Check (8,15,17)

Calculate $8^2 + 15^2 = 64 + 225 = 289$, and $17^2 = 289$. So $8^2 + 15^2 = 17^2$.

Step3: Check $(1,\sqrt{3},2)$

$\sqrt{3}$ is not an integer, so it is not a Pythagorean triple.

Step4: Check (9,12,16)

Calculate $9^2 + 12^2 = 81 + 144 = 225$, and $16^2 = 256$. $225
eq 256$, so it is not a triple.

Step5: Check (8,11,14)

Calculate $8^2 + 11^2 = 64 + 121 = 185$, and $14^2 = 196$. $185
eq 196$, so it is not a triple.

Step6: Check (20,21,29)

Calculate $20^2 + 21^2 = 400 + 441 = 841$, and $29^2 = 841$. So $20^2 + 21^2 = 29^2$.

Step7: Check (30,40,50)

Calculate $30^2 + 40^2 = 900 + 1600 = 2500$, and $50^2 = 2500$. So $30^2 + 40^2 = 50^2$.

Answer:

(8,15,17), (20,21,29), (30,40,50)