To construct the length √10 in a square-root spiral, a 1-unit perpendicular is added to which previous hypotenuse?

Correct answer: √9

The governing concept is the Pythagorean theorem used successively in a square-root spiral. At every stage, a perpendicular segment of length 1 unit is erected on the preceding hypotenuse. If that preceding hypotenuse is √n, then the new hypotenuse h satisfies h² = (√n)² + 1² = n + 1, so h = √(n + 1). For the desired length √10, we require n + 1 = 10, which gives n = 9. Hence the perpendicular must be drawn on the previous hypotenuse √9, making option B correct. Using √8 would produce √9; using √10 would produce √11; and using √11 would produce √12. Thus the other choices represent different stages.