An isosceles triangle, △ABC, has the measurements AB=BC=12. The segment BH is the altitude of △ABC, and BH=AH=CH=x. Which of the following correctly applies the Pythagorean Theorem to find x?
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, triangle △BHC is a right triangle with BH as the hypotenuse.
Using the Pythagorean Theorem in triangle △BHC, we have:
BH² = HC² + BC²
Substitute BH=x, HC=x, and BC=12:
x² = x² + 12²
x² = x² + 144
0 = 144
This equation is not correct, as it leads to an invalid result. The correct application of the Pythagorean Theorem to find x in this scenario would be:
BH² = AH² + AB²
Substitute BH=x, AH=x, and AB=12:
x² = x² + 12²
x² = x² + 144
0 = 144
This equation also leads to an invalid result. The correct application of the Pythagorean Theorem in this scenario would be to create a right triangle using the altitude BH and one of the base sides of the isosceles triangle. Or, use the fact that △BHC is a right triangle with BH as the hypotenuse, and apply the Pythagorean Theorem accordingly.