Question

Which of the following numbers form pythagorean triplet?
i) $2,3,4$
ii) $6,8,10$
iii) $9,10,11$
iv) $8,15,17$

• A. (ii), (iv)
• B. (i), (ii)
• C. (i), (ii), (iii)
• D. (ii), (iii)

Answer 1

Answer: (A)

(ii), (iv)

Three numbers $a,b,c$ form a pythagorean triplet ( where $c$ is the largest number ) if,

$c^2=a^2+b^2$

(1) $2,3,4$

$2^2+3^2=4+9=13$

$4^2=16$

$2^2+3^2\ne 4^2$

So, these numbers do not form pythagorean triplet.

(2) $6,8,10$

$6^2+8^2=36+64=100$

${10}^2=100$

$6^2+8^2={10}^2$

So, these numbers form pythagorean triplet.

(3) $9,10,11$

$9^2+{10}^2=81+100=181$

${11}^2=121$

$9^2+{10}^2\ne {11}^2$

So, these numbers do not form pythagorean triplet.

(4) $8,15,17$

$8^2+{15}^2=64+225=289$

${17}^2=289$

$8^2+{15}^2={17}^2$

So, these numbers form pythagorean triplet.