Question

which of the following could represent the length of 3 sides in a right triangle.

Answer 1

For a right triangle, according to Pythagorus theorem,

$c^2=a^2+b^2$

Here, c is the hypotenuse, a, b- length of other two sides.

The longer side is called the hypotenuse of a right triangle.

Conside option 1

1.6, 6.3, 6.5

6.5 is the longest side.

$\begin{gathered} 6.5^2=42.25 \\ 6.3^2+1.6^2=42.25 \\ 6.5^2=6.3^2+1.6^2 \end{gathered}$

Since side lengths 1.6, 6.3, 6.5 obeys Pythagorus theorem, the sides is of a right triangle.

The other given ste of sides does not follow Pythagorus theorem.

Consider 1.1, 6.3 , 6.5

$6.5^2\ne1.1^2+6.3^2$

Consider 4, 5, 6.

$6^2\ne4^2+5^2$

Consider 1.7, 14.4. 43.3.

$43.3^2\ne14.4^2+1.7^2$

Hence, 1.6, 6.3, 6.5 is correct.