Final answer:
To determine the length of BC and AC with AB = 12, the Pythagorean theorem is applied, suggesting that if ABC is a right isosceles triangle, BC would also be 12, and AC would be 12√2.
Step-by-step explanation:
To find the length of BC and AC when AB = 12, we need more information about the triangle ABC. Assuming triangle ABC is a right triangle with AB as one of the legs (since the question involves square roots, which are common in the application of the Pythagorean theorem), we could use the theorem to find the lengths of BC and AC.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):
a² + b² = c²
In our case, if AB = 12 and triangle ABC is isosceles with AB = BC, then:
AC = √(AB² + BC²)
AC = √(12² + 12²) = √(144 + 144) = √(288) = 12√2.
So, option B. BC = 12 and AC = 12√2 would be the correct lengths if triangle ABC is a right isosceles triangle. Without more context, we cannot definitively determine the lengths of BC and AC.