Question

pythagorean triple not a pythagorean triple
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answer bank
6, 8, 10 6, 8, 12 7, 24, 25 1, 2, 3

Explanation:

Step1: Recall Pythagorean rule

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

Step2: Test 6,8,10

$6^2 + 8^2 = 36 + 64 = 100 = 10^2$

Step3: Test 6,8,12

$6^2 + 8^2 = 36 + 64 = 100$, $12^2 = 144$, $100
eq 144$

Step4: Test 7,24,25

$7^2 + 24^2 = 49 + 576 = 625 = 25^2$

Step5: Test 1,2,3

$1^2 + 2^2 = 1 + 4 = 5$, $3^2 = 9$, $5
eq 9$

Answer:

Pythagorean triple: 6, 8, 10; 7, 24, 25
not a Pythagorean triple: 6, 8, 12; 1, 2, 3