Question

Use the image to answer the question.

On right triangle upper A upper C upper B, the altitude of vertex upper A is drawn as a solid line that extends from upper A to the hypotenuse, upper B upper C. The intersection of the altitude and upper B upper C is labeled upper D.

Use the steps from the proof of the Pythagorean Theorem to find x.

(1 point)
Responses

x=16912
x equals Start Fraction 169 over 12 End Fraction

x=169144
x equals Start Fraction 169 over 144 End Fraction

x=12
x equals 12

x=1698

Answer 1

Using the altitude relations from similar triangles:

AB^2 = BD·BC and AC^2 = CD·BC. Divide the two equations:

(AB^2)/(AC^2) = (BD·BC)/(CD·BC) = BD/CD.

Thus BD/CD = (AB/AC)^2. If AB = 13 and AC = 12, BD/CD = 13^2/12^2 = 169/144.

So x = 169/144.