Question

Which of the following is a Pythagorean triplet?
(a) $(2,3,5)$
(b) $(5,7,9)$
​​​​​​​(c) $(6,9,11)$
​​​​​​​(d) $(8,15,17)$

Answer 1

In three numbers, if square of the largest number is equal to sum of the squares of the other two numbers then they are said to be Pythagorean triplet.

(a)

$(2,3,5)$

$2^2=4$

$3^2=9$

$5^2=25$

$4+9\ne 25$

So $(2,3,5)$ not a Pythagorean triplet.

(b)

$(5,7,9)$

$5^2=25$

$7^2=49$

$9^2=81$

$81\ne 25+49$

So, $(5,7,9)$ not a Pythagorean triplet.

(c)

$(6,9,11)$

$6^2=36$

$9^2=81$

${11}^2=121$

$121\ne 36+81$

So, $(6,9,11)$ not a Pythagorean triplet.

(d)

$(8,15,17)$

$8^2=64$

${15}^2=225$

${17}^2=289$

$289=64+225$

i.e., ${17}^2=8^2+{15}^2$

So, $(8,15,17)$ is a Pythagorean triplet

Hence, Option D is correct.