Question

Which of the following is not a Pythagorean triplet?
a) 4,5,17 b) 6,8,10
c) 12,16,20 d) 24,7,25
please answer properly

Answer 1

Answer:

ans. : The first one

because, 4²+5²≠17²

Answer 2

Check for option(a).

Given: $4,5,17$.

Understand that, If $a,b,c$are three positive integers then they can be called Pythagorean Triplet only if it satisfies the following expression:$\[{a^2} + {b^2} = {c^{\bf{2}}}\]$.

Assume that, $a=4, b=5, c=17$.

Check whether the given numbers are a Pythagorean triplet.

$\[\begin{array}{l}{a^2} + {b^2} = {c^{\bf{2}}}.\\ \Rightarrow {4^2} + {5^2} = {17^2}\\ \Rightarrow 16 + 25 = 289\\ \Rightarrow 41 \ne 289\end{array}\]$

Observe that LHS is not equal to the RHS.

Therefore, $4,5,17$ is not a Pythagoran triplet.

Hence, this is the correct option.

Check for option(b).

Given: $6,8,10$.

Understand that, If $a,b,c$are three positive integers then they can be called Pythagorean Triplet only if it satisfies the following expression:$\[{a^2} + {b^2} = {c^{\bf{2}}}\]$.

Assume that, $a=6, b=8, c=10$.

Check whether the given numbers are a Pythagorean triplet.

$\[\begin{array}{l}{a^2} + {b^2} = {c^{\bf{2}}}.\\ \Rightarrow {6^2} + {8^2} = {10^2}\\ \Rightarrow 36 +64 = 100\\ \Rightarrow 100 = 100\end{array}\]$

Observe that LHS is equal to the RHS.

Therefore, $6,8,10$ is a Pythagoran triplet.

Hence, This is not the correct option.

Check for option(c).

Given: $12,16,20$.

Understand that, If $a,b,c$are three positive integers then they can be called Pythagorean Triplet only if it satisfies the following expression:$\[{a^2} + {b^2} = {c^{\bf{2}}}\]$.

Assume that, $a=12, b=16, c=20$.

Check whether the given numbers are a Pythagorean triplet.

$\[\begin{array}{l}{a^2} + {b^2} = {c^{\bf{2}}}.\\ \Rightarrow {12^2} + {16^2} = {20^2}\\ \Rightarrow 144 +256 = 400\\ \Rightarrow 280= 400\end{array}\]$

Observe that LHS is equal to the RHS.

Therefore, $12,16,20$ is a Pythagoran triplet.

Hence, This is not the correct option.

Check for option(d).

Given: $24,7,25$.

Understand that, If $a,b,c$are three positive integers then they can be called Pythagorean Triplet only if it satisfies the following expression:$\[{a^2} + {b^2} = {c^{\bf{2}}}\]$.

Assume that, $a=24, b=7, c=25$.

Check whether the given numbers are a Pythagorean triplet.

$\[\begin{array}{l}{a^2} + {b^2} = {c^{\bf{2}}}.\\ \Rightarrow {24^2} + {7^2} = {25^2}\\ \Rightarrow 576 +49 = 625\\ \Rightarrow 625 = 625\end{array}\]$

Observe that LHS is equal to the RHS.

Therefore, $24,7,25$ is a Pythagoran triplet.

Hence, This is not the correct option.

Final Answer:

The correct answer is option (a). i.e., $4,5,17$.