Question 4 of 11intermediate🔧 ApplyShort Answer2 marks

Can you think of different methods to construct a 90° angle at a given point on a line using a rope?

Correct Answer

Method 1: Perpendicular Bisector Method

Step 1: Fix the rope ends at equal distances from the given point O on the line.

Step 2: Pull the midpoint above and below to get points A and B on the perpendicular bisector.

Step 3: AB gives the 90° angle at O.

Method 2: 3-4-5 Triangle Method

Step 1: Take a rope of length 12 units divided into segments of 3, 4, and 5 units.

Step 2: Form a triangle with these segments as sides.

Step 3: The angle opposite the side of length 5 units is a right angle (90°).

Note: This ancient method was known in many civilizations including India.

Exercise: Figure it Out (Section 2) | Q: 2 | (Page Page 7)
For More Understanding

Explanation

The chapter discusses the Śulba-Sūtras which contain various methods for constructing perpendiculars. The perpendicular bisector method directly gives a 90° angle. Additionally, ancient Indian texts describe the use of right-angled triangles (like the 3-4-5 triangle) for constructing perpendiculars. The rope can be knotted at specific intervals to create these proportions, and when stretched to form a triangle, the right angle appears at the appropriate vertex.

Solution Steps

  1. Fix the rope ends at equal distances from the given point O on the line.

  2. Pull the midpoint above and below to get points A and B on the perpendicular bisector.

  3. AB gives the 90° angle at O.

  4. Take a rope of length 12 units divided into segments of 3, 4, and 5 units.

  5. Form a triangle with these segments as sides.

  6. The angle opposite the side of length 5 units is a right angle (90°).

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