# A triangle has sides with lengths of 47 kilometers, 54 kilometers, and 75 kilometers. Is it a right triangle?

Jun 7, 2018

$\text{not a right triangle}$

#### Explanation:

$\text{using the "color(blue)"converse of Pythagoras' theorem}$

$\text{if the triangle is right then}$

$\text{square on longest side "=" sum of square of other sides}$

${75}^{2} = 5625 \leftarrow \textcolor{b l u e}{\text{longest side}}$

${47}^{2} + {54}^{2} = 5125$

$\text{since "5625!=5125" not a right triangle}$