How do you determine if the lengths $4, sqrt26, 12$ form a right triangle?

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Answer 1 · 2017-03-08T01:23:35

See the entire solution process below:

We can use the Pythagorean Theorem to determine if these lengths form a right triangle.

The Pythagorean Theorem states, for a right triangle:

$a^2 + b^2 = c^2$ Where

$a$ and $b$ are legs of the right triangle
$c$ is the hypotenuse of the right triangle

Substituting $4$ and $sqrt(26)$ for $a$ and $b$ and substituting $12$ for $c$ gives:

$4^2 + (sqrt(26))^2 = 12^2$

$16 + 26 = 144$

$42 != 144$

These lengths for the sides of a triangle DO NOT form a right triangle.

How do you determine if the lengths 4, sqrt26, 124, sqrt26, 12 form a right triangle?