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Class 9MathematicsNumber SystemsSquare root spiralEasy
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In constructing a square root spiral, one side of each new right triangle is the previous hypotenuse. What length is taken for the other perpendicular side?

Answer and explanation

Correct answer: One unit

In a square root spiral, a perpendicular side of length 1 unit is added to the previous hypotenuse. Thus, the new hypotenuses represent \(\sqrt{2}, \sqrt{3}, \sqrt{4}\), and so on. Exam tip: the added side is always 1 unit.

Related tags

Number SystemsSquare Root SpiralRight TriangleIrrational NumbersGeometry ConstructionMathematicsClass 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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