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To make √10 in a square-root spiral, a 1-unit perpendicular is drawn on which previous hypotenuse?

Answer and explanation

Correct answer: √9

The governing construction rule says that a 1-unit perpendicular is drawn on the previous hypotenuse. If the previous hypotenuse is √n, then the Pythagorean theorem gives the next hypotenuse H by H² = (√n)² + 1² = n + 1. To obtain √10, we require n + 1 = 10, so n = 9. Therefore, the perpendicular must be drawn on √9, and option B is correct. Drawing it on √8 would produce √9, which is one stage too early. Drawing it on √10 would produce √11, and drawing it on √11 would produce √12. The answer is determined by identifying the immediately preceding squared value, not by choosing the target itself.

Related tags

Number-SystemsSquare-Root-SpiralConstruction-StepPythagorean-TheoremSquare Root SpiralNumber SystemsMathematicsClass 9 Mcq

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