Question

How do you determine whether the given lengths are sides of a right triangle 23, 18, 14?

Answer 1

`23`, `18` and `14` are not the sides of a right angled triangle.

Explanation:

If the triangle with sides `23`, `18` and `14` is a right angled triangle, `23` the largest side must be hypotenuse.

According to Pythagoras theorem, in a right angled triangle, the square of hypotenuse is equal to the sum of squares of other two sides. Let us check it.

`23^2=529` and `18^2+14^2=324+196=520`

Therefore `23^2>18^2+14^2`.

Hence, `23`, `18` and `14` are not the sides of a right angled triangle.

In fact as `23^2>18^2+14^2`, it is an obtuse angled triangle.