Question

Write a Pythagoras triplet whose member is 14:
$
  (a){\text{ 36,64}} \\
  (b){\text{ 48, 50}} \\
  (c){\text{ 8, 6}} \\
  (d){\text{ 17, 20}} \\
$

Answer 1

Hint:Consider the given member 14 as a variable say m, now use the direct formula $p = \left( {\dfrac{{{m^2}}}{4} + 1} \right),q = \left( {\dfrac{{{m^2}}}{4} - 1} \right)$ where p and q are the other members of the Pythagoras triplet.

Complete step-by-step answer:
Given data
One member of a Pythagorean triplet is 14.
Let m = 14
Now we have to find out the other two members.
Let other two members be (p) and (q)
Now the Pythagorean triplet is found according to property $\left( {\dfrac{{{m^2}}}{4} \pm 1} \right)$.
So first find out the square of the number
$ \Rightarrow {m^2} = {\left( {14} \right)^2} = 196$
Now divide by 4 in this number we have,
$ \Rightarrow \dfrac{{{m^2}}}{4} = \dfrac{{196}}{4} = 49$
Now add and subtract 1 in this number to get the required other members of the Pythagorean triplet.
$ \Rightarrow p = \dfrac{{{m^2}}}{4} + 1 = 49 + 1 = 50$
And
$ \Rightarrow q = \dfrac{{{m^2}}}{4} - 1 = 49 - 1 = 48$
So the other two members of the Pythagorean triplet are 48 and 50.
Hence option (B) is correct.

Note – A Pythagoras triplet in general consists of three positive integers a, b and c. So that these triplet follow the Pythagoras theorem that is ${a^2} + {b^2} = {c^2}$. In more practical terms the three numbers of Pythagoras triplet describe the three integer side’s lengths of a right triangle.