The square root spiral starts with a base triangle of sides 1 and 1, giving a hypotenuse of root 2. Each successive triangle adds a side of 1, yielding hypotenuses of root 2, root 3, root 4, and continuing sequentially.
Find the lengths of the hypotenuses of all the right triangles in Fig. 3.14 which is referred to as the square root spiral.
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In a standard square root spiral, the first right triangle has perpendicular sides of length 1 unit each. By the Pythagorean theorem, its hypotenuse is the square root of 2. The next right triangle is built using this hypotenuse as a base and adding a perpendicular side of 1 unit, making its hypotenuse the square root of 3. This mathematical pattern continues sequentially for all successive right triangles, creating hypotenuse lengths of root 2, root 3, root 4, root 5, and so on.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The world of numbers (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-3/