Question

which of the following is not a pythagorean triplet a) 3,4,5 b) 6,8,10c) 5,12,13d) 2,3,4​

Answer 1

The correct answer is option (d) 2,3,4

• The condition of the Pythagorean triplet is a²=b²+c², Now in the given options only d part, i.e 2,3,4 as 4²≠3²+2².
• Now,if we check the same condition for other options, 5² = 3²+4² , 25 = 25 , for this triplet the condition holds true, Now for 6,8,10  10² = 6²+8², 100 =100, for this triplet the condition holds true. Now , for 5,12,13 13² = 12²+5², 169 = 169. Therefore this condition holds true for all triplets except 2,3,4.

Answer 2

Step-by-step explanation:

As we know that,

Pythagorean triplets are set of such three number in which the additional of the square of two smaller number will be equal to square of the greater number.

let a, b, and c are any pythagorean triplet, then $a^2+b^2=c^2$

So, for determining that which one is not the pythsgorean triplet, let us check all the given numbers in the options:

$Option\:(a)\\3,4,5\Rightarrow 3^2+4^2=9+16=25=5^2 (Pythagorean\:triplet)\\Option\:(b)\\6,8,10\Rightarrow 6^2+8^2=36+64=100=10^2 (Pythagorean\:triplet)\\Option\:(c)\\5,12,13\Rightarrow 5^2+12^2=25+144=169=13^2 (Pythagorean\:triplet)\\Option\:(d)\\2,3,4 \Rightarrow 2^2+3^2=4+9=13 \neq 4^2 (Not\:a\:Pythagorean\:triplet)$

Answer:

Hence, from above, we can clearly conclude that the set of numbers given in (d) i.e., 2, 3, 4 are not pythagorean triplets numbers.