- A9.3 units
- B units
- C units
- D units
Step-by-Step Solution
BD is the geometric mean of the two parts of the diameter: BD = . This is the standard way to locate the square root of a decimal number on the number line.
Answer: D) units
A segment AB of length 9.3 units is extended to C so that BC = 1 unit. A semicircle is drawn with AC as diameter, and the perpendicular to AC at B meets the semicircle at D. What length does BD represent?
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).
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