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=72
x equals 72

x=62–√
x equals 6 Start Root 2 End Root

x=122–√
x equals 12 Start Root 2 End Root

x=6

1 answer

To find the correct application of the Pythagorean Theorem for triangle ABC, we note that AB=BC=12 and BH is the altitude from B to AC, with AH=CH=x.

Since ABC is isosceles, AC=AH+CH=x+x=2x.

Now applying the Pythagorean Theorem in triangle ABH, we have:

AB2=AH2+BH2

Plugging in the values:

122=x2+BH2

Since BH=x:

122=x2+x2

This becomes:

144=2x2

Dividing by 2 gives:

72=x2

Thus:

x=72=62

Therefore, the correct response is:

x = 6√2 (x equals 6 Start Root 2 End Root).