Question

Write a Pythagorean triplet one of whose member is 10

Answer 1

Answer:

10 , 24 & 26 is a Pythagorean triplet whose smallest number is 10.

Answer 2

$\huge{\underline{\mathtt{\red{S}\pink{O}\green{L}\blue{U}\purple{T}\orange{I}\pink{O}\red{N ᭄}}}}$

We know 2m, m^2-1 and m^2+1 form a Pythagorean triplet.

Given,

One member of triplet= 10

Then,

$\sf1) \: {2m = 10}$

$\implies\sf{m= 5}$

$\sf2) \: { {m}^{2} - 1}$

$\implies\sf{( {5}^{2} - 1)}$

$\implies\sf{25-1}$

$\implies\sf{24}$

$\sf 3) \: { {m^{2} + 1}}$

$\implies\sf {( {5}^{2} + 1)}$

$\implies\sf {25+1}$

$\implies\sf {26}$

Hence, 10,24 and 26 form a Pythagorean triplet.

$\huge\sf{\underline{\green{Verification}}}$

$\sf{ {10}^{2} = 100}$

$\sf{ {24}^{2} = 576}$

$\sf{ {26}^{2} = 676}$

$\implies\sf{676=576+100}$

$\implies\sf\purple{ {26}^{2} = {24}^{2} + {10}^{2} }$