# How do you use the Pythagorean Theorem to determine if the three numbers could be the measures of the sides of a right triangle assuming that the largest is the hypotenuse: 72, 17, 19?

Apr 3, 2016

If you arrange the length of the sides in non-decreasing order, such as $a \le b \le c$, just check whether the relation

${c}^{2} = {a}^{2} + {b}^{2}$

is true.

For this case

• $a = 17$
• $b = 19$
• $c = 72$

Plugging in, the left hand side gives

${c}^{2} = {72}^{2}$

$= 5184$

The right hand side gives

${a}^{2} + {b}^{2} = {17}^{2} + {19}^{2}$

$= 289 + 361$

$= 650 \ne 5184$

Since the equality does not hold, there is no right-angle triangle with sides measuring 17, 19 and 72.