Answer: LAST OPTION.
Step-by-step explanation:
The Pythagorean Theorem states the following relationship between the three sides of a triangle that has an angle of 90 degrees, known as "Right triangle":
[tex]a^2=b^2+c^2[/tex]
Where "a"is the hypotenuse and "b" and "c" are the legs of the right triangle.
If the triangle ABC is a right triangle then AB must be equal to [tex]BC^2+AC^2[/tex], then, you need to substitute the values into [tex]a^2=b^2+c^2[/tex] to check this:
[tex]12^2=5^2+10^2\\144\neq 125[/tex]
Then the triangle ABC is not a right triangle.
Therefore, the statement that justifies why this triangle is not a right triangle is:
[tex]5^2+10^2\neq 12^2[/tex]
