Question

Which set of sides would make a right triangle? 5,10,12 8,10,12 5,12,13 4,5,6

Answer 1

Our answer are the sides 5,12 and 13 which represent a Pythagoraen triple

The sides of a triangle that would make a right-triangle are collectively called a Pythagorean triple

These measures stem from the Pythagoras theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides

At any point in time, the hypotenuse refers to the longest side in the triangle

So basically, to get the correct answer from these options, if we square the longest side, and the sum of the squares of the two other sides equal the square of this longest side, the side that provides us with this would be our answer

So let us consider the options individually;

`\begin{gathered} 12^2\text{ }\\e5^2+10^2 \\ \\ 12^2\\e8^2+10^2 \\ \\ 6^2\text{ }\\e4^2+5^2 \\ \\ \text{But;} \\ \\ 13^2=5^2+12^2 \end{gathered}`