To construct √18 in a square-root spiral, on which previous hypotenuse is a 1-unit perpendicular drawn?

Correct answer: √17

The governing rule is that each new hypotenuse is formed by drawing a perpendicular of length 1 unit to the preceding hypotenuse. If the preceding hypotenuse is √n, the Pythagorean theorem gives H² = (√n)² + 1² = n + 1, so the new hypotenuse is √(n + 1). For the target √18, we solve n + 1 = 18 and obtain n = 17. Thus the perpendicular must be drawn on √17, making option B correct. A perpendicular on √16 would produce √17, not √18. One on √18 would produce √19, and one on √19 would produce √20. These distractors represent adjacent stages and therefore test whether the construction rule has been applied in the correct direction.