Question

Which of the following triplets are Pythagorean ?
$(3,4,5),(6,7,8),(10,24,26),(2,3,4).$

Answer 1

Let the smallest even number be $2$m

(i) $(3,4,5)$

$2m=4$

$\Rightarrow m=2$

$m^2-1=4-1=3$

$m^2+1=4+1=5$

$\therefore (3,4,5)$ is a Pythagorean triplet.

(ii) $(10,24,26)$

$2m=10$

$\Rightarrow m=5$

$m^2-1=25-1=24$

$m^2+1=25+1=26$

$\therefore (10,24,26)$ is not a Pythagorean triplet.

(iii) $(6,7,8)$

$2m=6$

$\Rightarrow m=3$

$m^2-1=9-1=8$

$m^2+1=9+1=10$

$\therefore (6,7,8)$ is not a Pythagorean triplet.

(iv) $(2,3,4)$

$2m=2$

$\Rightarrow m=1$

$m^2-1=1-1=0$

$m^2+1=1+1=2$

$\therefore (2,3,4)$ is not a Pythagorean triplet.