# Is a triangle with sides of 6, 8, and 10, a right triangle?

May 24, 2016

yes-a right triangle.

#### Explanation:

$\textcolor{b l u e}{\text{Pythagoras' theorem}}$ states that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.

The$\textcolor{b l u e}{\text{ Converse}}$ of this statement is 'if the square on the longest side of a triangle equals the sum of the squares on the other two sides then the triangle is right'.

Here the longest side = 10 $\Rightarrow {10}^{2} = 100$

and ${6}^{2} + {8}^{2} = 36 + 64 = 100$

This satisfies the converse condition hence the triangle is right.