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?

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Answer 1 · 2016-04-03T06:16:12

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

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

is true.

For this case

Plugging in, the left hand side gives

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

$= 5184$ $= 5184$

The right hand side gives

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

$= 289 + 361$ $= 289 + 361$

$= 650 \neq 5184$ $= 650 != 5184$

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