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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Side upper A upper B is labeled 12. Side upper B upper C is also labeled 12. Line upper B upper H, and line segments upper A upper H, and upper H upper C, are all labeled x.


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=6

x equals 6

x=6√2

x equals 6 Start Root 2 End Root

x=12√2

x equals 12 Start Root 2 End Root

x=72

x equals 72
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Answer 1

Use right triangle ABH: AH = x and BH = x are legs and AB = 12 is the hypotenuse. By Pythagoras,

x^2 + x^2 = 12^2
2x^2 = 144
x^2 = 72
x = √72 = 6√2.

So x = 6√2.