Question

Write the Pythagorean triplet if one number is $14$?

Answer 1

Determine the Pythagorean triplet.

A Pythagorean triple consists of three positive integers $a,b,$ and $c$, such that $a^2+b^2=c^2$.

Given number $=14$

Let

$$\begin{gathered} 2m=14 \\ \Rightarrow m=\frac{14}{2} \\ \Rightarrow m=7 \end{gathered}$$

Calculate the second number:

$$\begin{gathered} m^2+1=7^2+1 \\ \Rightarrow =49+1 \\ \Rightarrow =50 \end{gathered}$$

Calculate the third number:

$$\begin{gathered} m^2-1=7^2-1 \\ \Rightarrow =49-1 \\ \Rightarrow =48 \end{gathered}$$

Apply the Pythagorean theorem to check the value:

$$\begin{gathered} A^2+B^2=C^2 \\ \Rightarrow {14}^2+{48}^2={50}^2 \\ \Rightarrow 196+1304=2500 \\ \Rightarrow 2500=2500 \end{gathered}$$

Hence, The triplet is $14,48,and50$.