Question

Write the Pythagorean triplet whose smallest member is $8$?

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:

$$\begin{gathered} 2m=8 \\ \Rightarrow m=\frac{8}{2} \\ \Rightarrow m=4 \end{gathered}$$

Consider the second value:

$$\begin{gathered} m^2+1=4^2+1 \\ \Rightarrow =16+1 \\ \Rightarrow =17 \end{gathered}$$

Consider the third value:

$$\begin{gathered} m^2-1=4^2-1 \\ \Rightarrow =16-1 \\ \Rightarrow =15 \end{gathered}$$

Hence, the Pythagorean triplet is $8,15,$ and $17$.