Question

which of the following is not a pythagorean triple? a. 15, 36, 39 b. 24, 45, 51 c. 21, 72, 76 d. 18, 24, 30

Explanation:

Step1: Recall Pythagorean rule

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

Step2: Test Option A

$15^2 + 36^2 = 225 + 1296 = 1521$, $39^2 = 1521$. So $15^2+36^2=39^2$.

Step3: Test Option B

$24^2 + 45^2 = 576 + 2025 = 2601$, $51^2 = 2601$. So $24^2+45^2=51^2$.

Step4: Test Option C

$21^2 + 72^2 = 441 + 5184 = 5625$, $76^2 = 5776$. $5625
eq 5776$.

Step5: Test Option D (verify)

$18^2 + 24^2 = 324 + 576 = 900$, $30^2 = 900$. So $18^2+24^2=30^2$.

Answer:

C. 21, 72, 76