Question

Use the image to answer the question.

An isosceles triangle upper A upper B upper C. Vertex upper A is on the bottom left, vertex upper B is at the top, and vertex upper C is on the bottom right. A line extends from vertex B to the middle of the base, creating a right angle labeled upper H.
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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?

(1 point)
Responses

x=62–√

x equals 6 Start Root 2 End Root

x=72

x equals 72

x=6

x equals 6

x=122–√

Answer 1

In right triangle ABH, AB = 12 is the hypotenuse and AH = BH = x are the legs. By the Pythagorean Theorem:

12^2 = x^2 + x^2 = 2x^2 → x^2 = 72 → x = √72 = 6√2.

So the correct choice is x = 6√2.