Question

Write the Pythagorean triplet whose one of the numbers is $4$.

Answer 1

Determine the Pythagorean triple.

A Pythagorean triple consists of three positive integers$a,b,$ and $c$, such that $a^2+b^2=c^2$. Here, $a$ is the perpendicular, $b$ is the base and $c$ is the hypotenuse of the right-angled triangle.

Use the general formula of the Pythagorean triple.

$2m,m^2–1,m^2+1$

Consider the first value:

$$\begin{gathered} 2m=4 \\ \Rightarrow m=\frac{4}{2} \\ \therefore m=2 \end{gathered}$$

Consider the second value:

$$\begin{gathered} m^2+1=2^2+1 \\ =4+1 \\ =5 \end{gathered}$$

Consider the third value:

$$\begin{gathered} m^2-1=2^2-1 \\ =4-1 \\ =3 \end{gathered}$$

Hence, the Pythagorean triplet is $3,4,\text{and}5$.