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Subjects
Class 9MathematicsNumber SystemsSquare root spiralEasy
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While constructing a square root spiral, a student draws the new side in the same direction from the endpoint of the previous hypotenuse. How should the new unit-length side be drawn to keep the spiral correct?

Answer and explanation

Correct answer: Perpendicular to the previous hypotenuse

Each added triangle must be right-angled. Drawing a unit side perpendicular to the previous hypotenuse gives the next hypotenuse using Pythagoras’ theorem. A parallel side does not form a right angle. Exam tip: mark the new unit side perpendicular first.

Related tags

Number SystemsSquare Root SpiralPythagoras TheoremGeometrical ConstructionIrrational NumbersMathematicsClass 9 Mcq
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10 more MCQs
  1. 1In a square root spiral, which segment is drawn at the end of the previous hypotenuse to form a new right triangle?
  2. 2In a square root spiral, what is the hypotenuse of the first right triangle made with base (1) unit and perpendicular (1) unit?
  3. 3If a perpendicular of length 1 unit is drawn at the end of a hypotenuse of length √2, what will be the length of the next hypotenuse?
  4. 4In a square root spiral, after the hypotenuse (\sqrt{3}), which length is obtained by adding a (1) unit perpendicular?
  5. 5Each new triangle in a square root spiral is of which type?
  6. 6In a square root spiral, how long is the new perpendicular side usually kept in each new triangle?
  7. 7Which theorem is mainly used to find the hypotenuse in a square root spiral?
  8. 8Why is each new 1-unit line segment drawn perpendicular to the previous hypotenuse in a square root spiral?
  9. 9Starting from (\sqrt{1}) in a square root spiral, which is the third hypotenuse?
  10. 10In a square root spiral, the line segment representing \(\sqrt{7}\) lies between which two consecutive whole numbers?
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