Question 2 of 14intermediate🔧 ApplyLong Answer3 marks

[Śulba-Sūtras] Give a method to transform a triangle into a rectangle of equal area.

Correct Answer

Method: To transform a triangle into a rectangle of equal area:

Step 1: Take triangle ABC with base b and height h.

Step 2: Area of triangle = ½ × b × h.

Step 3: Construct rectangle with base = b and height = h/2.

Step 4: Area of rectangle = b × (h/2) = ½ × b × h = Area of triangle.

Alternative Method (by dissection): Cut the triangle at mid-height and rearrange the pieces to form a rectangle.

Exercise: Figure it Out (Section 2) | Q: 5 | (Page Page 11)
For More Understanding

Explanation

The chapter discusses dissection methods from Śulba-Sūtras. A triangle can be converted to a rectangle by taking half the height and keeping the same base, or by cutting and rearranging pieces.

Solution Steps

  1. Step 1: Take triangle ABC with base b and height h.

  2. Step 2: Area of triangle = ½ × b × h.

  3. Step 3: Construct rectangle with base = b and height = h/2.

  4. Step 4: Area of rectangle = b × (h/2) = ½ × b × h = Area of triangle.

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