Question

Do the side lengths 10, 16, and 19 form a Pythagorean triple? Explain

Answer 1

A Pythagorean triple consists of 3 integer numbers, say, a,b and c, such that

`a^2+b^2=c^2`

From the given information, we can see that

`\begin{gathered} a=10 \\ b=16 \\ c=19 \end{gathered}`

So, if these 3 numbers are a Pythagorean triple, then the following equality must be fulfilled:

`10^2+16^2=19^2`

which gives

`\begin{gathered} 100+256=361 \\ \end{gathered}`

so we have obtained that

`356=361`

which is an absurd result. This means that the given numbers do not form a Pythagorean triple