# Is a triangle with sides of length 10 cm 24 cm 27 cm a right triangle?

Mar 3, 2016

not a right triangle

#### Explanation:

Use the $\textcolor{b l u e}{\text{ Converse of Pythagoras' Theorem }}$

Pythagoras' Theorem states ' the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other
2 sides '

The converse of this is ' if the square on the longest side of a triangle equals the sum of the squares on the other 2 sides then the triangle is right'.

$\text{(longest side)^2} = {27}^{2} = 729$

and ${10}^{2} + {24}^{2} = 100 + 576 = 676$

now 729 ≠ 676 , hence not a right triangle.