- A√6 units
- B6 units
- C√5 units
- D√7 units
Step-by-Step Solution
Each step adds to the square of the hypotenuse: , … so units.
Answer: A) √6 units
In the square-root spiral, OP1 = 1 unit and each outer side P1P2, P2P3, … is 1 unit, drawn at right angles to the previous hypotenuse. What is the length of the orange segment OP6?
Class 9Number SystemsNumber Systems
Key idea: Representing real numbers on the number line
Every real number has a unique location on the number line.
- Rationals: easy to plot. → 3 quarters past 0.
- Irrationals like can be plotted geometrically: a right triangle with legs 1 and 1 has hypotenuse (Pythagoras). Use a compass to mark off on the number line from 0.
You can extend this — from a triangle with legs and 1, from legs 2 and 1, etc. (the spiral of Theodorus).
- Rationals: easy to plot. → 3 quarters past 0.
- Irrationals like can be plotted geometrically: a right triangle with legs 1 and 1 has hypotenuse (Pythagoras). Use a compass to mark off on the number line from 0.
You can extend this — from a triangle with legs and 1, from legs 2 and 1, etc. (the spiral of Theodorus).
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Number Systems practice questions
More Class 9 Number Systems practice
OA equals the diagonal of the unit square, AB = 1 unit is drawn perpendicular to the…Successive magnification is used to locate a decimal on the number line: the orange part…Four segments are drawn on squared paper where each square is 1 cm × 1 cm. Which segment…Points A and B are marked on the number line; the small marks are 0.1 apart. Which of…To locate √9.3, AB = 9.3 units and BC = 1 unit are marked on a line, O is the midpoint…