Classify the triangle based on the side lengths 10, 12 and 23.

I am assuming 10 and 12 are the legs and 23 is the hypotenuse?

With that said, we can use the pythagorean theorem a^2+b^2=c^2

a^2+b^2=c^2 = Right triangle

a^2+b^2 < c^2 = abtuse

a^2+b^2 > c^2 = acute

10^2 + 12^2 = 23^2

244 = 529

244 < 529

It is abtuse