Question 9 of 14intermediate🔧 ApplyLong Answer3 marks

[Śulba-Sūtras] Give a method to convert a rectangle into an isosceles triangle by dissection.

Correct Answer

Step 1: Take rectangle with length l and width w.

Step 2: Mark the midpoint of one of the longer sides.

Step 3: From this midpoint, draw lines to the two opposite corners of the rectangle.

Step 4: Cut along these lines to create two right triangles.

Step 5: Join these triangles along their equal legs to form an isosceles triangle with base = 2l and height = w/2, or base = l and height = w depending on the arrangement.

Exercise: Figure it Out (Section 4) | Q: 8 | (Chapter: Page 17)
For More Understanding

Explanation

The chapter discusses dissection methods from Śulba-Sūtras. The reverse transformation of converting rectangle to isosceles triangle involves cutting and rearranging pieces.

Solution Steps

  1. Step 1: Take rectangle ABCD with AB = l, BC = w.

  2. Step 2: Find midpoint M of side AD.

  3. Step 3: Join M to B and M to C.

  4. Step 4: Cut along MB and MC to get two right triangles.

  5. Step 5: Rearrange to form isosceles triangle.

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