Question

prove that 2a,2b,2c are in pythagorean triplet .if a,b,c from a pythagorean triplet?​

Answer 1

Step-by-step explanation:

Let the triplet be 3, 4, and 5

Then:-

${a}^{2} + {b}^{2} = {c}^{2} . \: (pythagoras \: theorem)$

$= > {3}^{2} + {4}^{2} = {5}^{2}$

We need to prove that:-

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

$= > 2( {3}^{2} ) + 2( {4}^{2} ) = 2( {5}^{2} )$

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

$= > 36 + 64 = 100$

$= > 100 = 100$

Therefore , we can imply upon the idea that 2a, 2b and 2c are in a Pythagorean Triplet, if a, b and c form a Pythagorean Triplet.

$hence \: proved \:$

Hope it helps...