Question

An isosceles triangle, △ABC
△
𝐴
𝐵
𝐶
, has the measurements AB=BC=12
𝐴
𝐵
=
𝐵
𝐶
=
12
. The segment BH
𝐵
𝐻
is the altitude of △ABC
△
𝐴
𝐵
𝐶
, and BH=AH=CH=x
𝐵
𝐻
=
𝐴
𝐻
=
𝐶
𝐻
=
𝑥
. Which of the following correctly applies the Pythagorean Theorem to find x?

(1 point)
Responses

x=72
𝑥
=
72

x equals 72

x=62–√
𝑥
=
6
2

x equals 6 Start Root 2 End Root

x=122–√
𝑥
=
12
2

x equals 12 Start Root 2 End Root

x=6

Answer 1

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

12^2 = x^2 + x^2 = 2x^2
144 = 2x^2
x^2 = 72
x = sqrt(72) = 6√2.

So the correct choice is x = 6√2.