Question

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

Answer 1

I do not think so.

Explanation:

Try with Pythagora's Theorem:

`50^2=13^2+12^2`
`2500=169+144=313` NO

Answer 2

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 >= c`

`12 + 13 = 25 < 50`

Answer 3

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

`color(white)("XXXX")` `50^2 = 2500`

`color(white)("XXXX")`1`3^2+12^2 = 169+144 = 313`

`50^2!=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.

Answer 4

No, not according to the Pythagorean theorem.

Explanation:

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`