Before constructing (\sqrt{18}) in a square root spiral, which hypotenuse will already be constructed?

Correct answer: (\sqrt{17})

The direct answer is B: \(\sqrt{17}\). In the spiral, the construction proceeds one step at a time. If a hypotenuse of length \(\sqrt{17}\) has already been made, a new perpendicular side of length 1 is attached to it. By Pythagoras theorem, the new hypotenuse satisfies \(c^2=(\sqrt{17})^2+1^2=17+1=18\), so its length is \(\sqrt{18}\). Therefore the immediately preceding hypotenuse is \(\sqrt{17}\). Option A, \(\sqrt{16}\), is one more step earlier and is not the hypotenuse immediately before \(\sqrt{18}\). Option B is correct because adding the next unit perpendicular side to \(\sqrt{17}\) produces \(\sqrt{18}\). Option C, \(\sqrt{18}\), is the length being constructed, not the one already constructed before it. Option D, \(\sqrt{19}\), comes after \(\sqrt{18}\), so it cannot be the previous hypotenuse. The sequence is \(\sqrt{16},\sqrt{17},\sqrt{18},\sqrt{19}\); “before” means move one place left.