Question

Which of the following is a Pythagorean triplet?

• A. (4, 8, 10)
• B. (8, 15, 17)
• C. (7, 24, 27)
• D. (7, 10, 15)

Answer 1

The correct option is B (8, 15, 17)

There can be infinite pythagorean triplets. But we are to check the given four triplets.
Let's check them one-by-one to check which ones are the pythagorean triplets and which ones are not.

a) (4, 8, 10)
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $4^2$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $8^2$ = 16 + 64 = 80 ≠ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${10}^2$
Therefore, (4, 8, 10) is not a yhtagorean triplet.

b) (8, 15, 17)
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $8^2$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${15}^2$ = 64 + 225 = 289 = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${17}^2$
Therefore, (8, 15, 17) is a Pythagorean triplet.

c) (7, 24, 27)
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $7^2$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${24}^2$ = 49 + 576 = 625 = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${25}^2$
Therefore, (7, 24, 27) is not a Pythagorean triplet but (7, 24, 25) is one of the Pythagorean triplets.

d) (7, 10, 15)
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $7^2$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${10}^2$ = 49 + 100 = 149 ≠ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${15}^2$
Therefore, (7, 10, 15) is also not a Pythagorean triplet.