# How do you use the Pythagorean Theorem to determine if the following triangle with sides a, b, & c is a right triangle: a=5, b=10, c=15?

Apr 17, 2016

${c}^{2} \ne {a}^{2} + {b}^{2}$, therefore, this cannot be a right triangle.

#### Explanation:

The Pythagorean Theorem applies to right angle triangles, where the sides $a$ and $b$ are those which intersect at right angle. The third side, the hypotenuse, is then $c$

To test whether the given lengths of sides create a right triangle, we need to substitute them into the Pythagorean Theorem - if it works out then it is a right angle triangle:

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

${15}^{2} \ne {5}^{2} + {10}^{2}$
$225 \ne 25 + 100$
$225 \ne 125$

In reality, if $a = 5$ and $b = 10$ then $c$ would have to be

${c}^{2} = 125$
$c = \sqrt{125} = 5 \sqrt{5} \cong 11.2$

which is smaller than the proposed value in the question. Therefore, this cannot be a right triangle.