If a triangle has the side lengths of 10, 7, and 12.3 would it be a right triangle

No it would not.

Because the sum of the squares of the two short sides is not equal to the square of the largest side.

7^2 + 10^2 = / = 12.3^2

Answer: No, it is not a right triangle

Explanation:

Let's assume we have a right triangle. If that's the case, then

a^2+b^2 = c^2

would be a true equation where

a = 10 and b = 7 are the two legs of the triangle

c = 12.3 is the hypotenuse (longest side)

Plug the values in and see what happens after we simplify

a^2 + b^2 = c^2

10^2 + 7^2 = (12.3) ^2

100 + 49 = 151.29

149 = 151.29

Both sides are not the same number, so this given triangle is not a right triangle.