Question

Which among the following are Pythagorean triplets?
$\left(i\right)1,1,2$
$\left(ii\right)3,4,6$
$\left(iii\right)12,16,20$
$\left(iv\right)15,8,17$
(2 marks)

Answer 1

$\text{Pythagorean triplets are set of three}\text{positive integers a, b, c such that,}{a}^2+b^2=c^2.$

$1^2+1^2=1+1=2\therefore 1^2+1^2\ne 2^2.$
$\text{Hence, the numbers 1, 1, 2}\text{do not form Pythagorean triplet.}$
(0.5 marks)
$3^2+4^2=9+16=25=5^2.\therefore 3^2+4^2\ne 6^2\text{Hence, the numbers 3, 4 and 6}\text{does not form a Pythagorean triplet.}$
(0.5 marks)
${12}^2+{16}^2=144+256=400={20}^2\text{Hence, the numbers 12, 16 and 20}\text{form a Pythagorean triplet.}$
(0.5 marks)
${15}^2+8^2=225+64=289={17}^2.\text{Hence, the numbers 15, 8 and 17}\text{form a Pythagorean triplet.}$
(0.5 marks)
$\text{Therefore, the numbers 12, 16, 20 and 15, 8, 17}\text{form Pythagorean triplets.}$