How do you determine if the lengths 8, 31.5, 32.5 form a right triangle?

Aug 28, 2017

$\text{right triangle}$

Explanation:

$\textcolor{b l u e}{\text{Converse theorem of Pythagoras}}$

$\text{if the "("longest side" )^2" is equal to the sum of the square}$
$\text{of the other 2 sides then it is a right triangle}$

${\left(\text{longest side}\right)}^{2} = {\left(32.5\right)}^{2} = 1056.25$

${8}^{2} + {\left(31.5\right)}^{2} = 64 + 992.25 = 1056.25$

$\Rightarrow \text{the 3 lengths form a right triangle}$