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

Jun 10, 2016

$23$, $18$ 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.