# Is a triangle with sides of lengths 32, 60, and 68 a right triangle?

Apr 1, 2018

$\text{yes a right triangle}$

#### Explanation:

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

• " if the square of the longest side is equal to the sum of"
$\textcolor{w h i t e}{\times x} \text{the other two sides squared then it is a right triangle}$

$\text{longest side } = 68$

$\Rightarrow {68}^{2} = 4624$

$\Rightarrow {32}^{2} + {60}^{2} = 1024 + 3600 = 4624$

$\Rightarrow 32 , 60 \text{ and "68" are the sides of a right triangle}$