Answer:
No
Explanation:
A triangle with sides 6, 12, 13 is not a right triangle. We can know this by using the Pythagorean Theorem.
The two shorter sides are called legs. The longest side is the hypotenuse. In a right triangle this formula is true:
leg^2+ leg^2 = hypotenuse^2
Let's test our triangle.
6^2 + 12^2 =? 13^2
36 + 144 =? 169
180 =? 169 Nope!
The equation doesn't work so this is not a right triangle.
Also, a shortcut is to memorize some Pythagorean Triples.
These are triangle side lengths that are whole numbers, easily memorized and known to be right triangles. Such as 3,4,5 or 8,15,17 or (this one will help us) 5,12,13.
5,12,13 is a right triangle. So the shortcut is that 6,12,13 would obviously not be a right triangle. Triples are a shortcut. But you can always use Pythagorean Thm to check.