An isosceles triangle, ABC, has the measurements AB = BC = 12. The

Question

segment BH is the altitude of AABC, and BH = AH = CH = x. Which of the
following correctly applies the Pythagorean Theorem to find x?

Answer 1

Since the triangle is isosceles, we can see that angle B is a right angle.

Using the Pythagorean Theorem, we can write:

AB^2 = AH^2 + BH^2

Substitute the values given:

12^2 = x^2 + x^2

144 = 2x^2

Divide by 2:

72 = x^2

Take the square root of both sides:

x = √72

Therefore, x = 6√2.

So, the correct answer is:

x = 6√2