Question

Write a Pythagorean triplet whose one number is 14.

Answer 1

Hint: We use the general formula for Pythagorean triplet and equate the given number. Using the substitution method we find two other numbers that conclude the Pythagorean triplet.
* A Pythagorean triplet \[(a,b,c)\] is given by the formula \[(2m,{m^2} - 1,{m^2} + 1)\]

Complete step-by-step answer:
We are given one of the numbers is 14
Let us assume the value of \[a = 14\]
From the formula of Pythagorean triplet we know a triplet \[(a,b,c)\] is given by the
formula\[(2m,{m^2} - 1,{m^2} + 1)\].
\[ \Rightarrow 2m = 14\]
Divide both sides of the equation by 2
\[ \Rightarrow \dfrac{{2m}}{2} = \dfrac{{14}}{2}\]
\[ \Rightarrow m = 7\] ……….… (1)
Now we know value of \[b = {m^2} - 1\]
Substitute the value of ‘m’ from equation (1) in value of ‘b’
\[ \Rightarrow b = {(7)^2} - 1\]
Square the term in RHS of the equation
\[ \Rightarrow b = 49 - 1\]
Calculate the difference in RHS of the equation
\[ \Rightarrow b = 48\] …….… (2)
Now we know value of \[c = {m^2} + 1\]
Substitute the value of ‘m’ from equation (1) in value of ‘c’
\[ \Rightarrow c = {(7)^2} + 1\]
Square the term in RHS of the equation
\[ \Rightarrow c = 49 + 1\]
Calculate the sum in RHS of the equation
\[ \Rightarrow c = 50\] ….….… (3)
From equations (2) and (3) the value of \[b = 48,c = 50\]
Since we know that one of the number is 14, so the value of \[a = 14\]

\[\therefore \]Pythagorean triples is \[(14,48,50)\]

Note: Students might try to solve for the Pythagorean triplet by using the Pythagoras theorem and writing sum of squares of two numbers equal to square of a third number where they might take any number as 14 and try solving the equation. This is the wrong approach as we will not reach a final answer, we will just get a relation between two of the missing numbers. Since we are required to find the other two numbers we will directly use the formula for Pythagorean triplet.