# Can 50mm, 13mm and 12mm be a right triangle?

Jun 10, 2015

I do not think so.

#### Explanation:

Try with Pythagora's Theorem:

${50}^{2} = {13}^{2} + {12}^{2}$
$2500 = 169 + 144 = 313$ NO

Jun 10, 2015

It cannot even be a triangle let alone a right angled one.

#### Explanation:

If $a$, $b$ and $c$ are the lengths of the sides of a triangle and $c$ is the largest value, then $a + b \ge c$

$12 + 13 = 25 < 50$

Jun 10, 2015

A triangle with sides 50mm, 13mm, and 12mm can not form a right triangle

#### Explanation:

By the Pythagorean Theorem, to be a right triangle:
the square of the longest side
must be equal to
the sum of the squares of the other two sides

$\textcolor{w h i t e}{\text{XXXX}}$${50}^{2} = 2500$

$\textcolor{w h i t e}{\text{XXXX}}$1${3}^{2} + {12}^{2} = 169 + 144 = 313$

${50}^{2} \ne {13}^{2} + {12}^{2}$

Also
Note that no triangle can exist with sides 50mm, 13mm, and 12mm.
Explanation 2:
To form a triangle, every side must be less than the sum of the other two sides.
Picture a line segment of length 50mm with a line segment of 13 mm attached to one end and a line segment of 12 mm attached to the other end. The 13mm and 12mm line segments can not reach far enough to touch each other.

Jun 24, 2015

If you plug in the side lengths into the Pythagorean theorem, assuming that $50$ is the hypotenuse and that side lengths are $13$ and $12$, you can calculate whether the triangle is a right triangle or not.
${13}^{2} + {12}^{2} = 313$, while $\sqrt{313}$ certainly doesn't equal ${50}^{2}$.
${a}^{2} + {b}^{2} = {c}^{2}$