Question 12 of 14intermediate🔧 ApplyLong Answer3 marks

Give a method to convert a rectangle into a rhombus of equal area using dissection.

Correct Answer

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

Step 2: For a rhombus with diagonals d₁ and d₂: Area = ½ × d₁ × d₂

Step 3: Set areas equal: ½ × d₁ × d₂ = l × w ∴ d₁ × d₂ = 2lw

Step 4: Choose appropriate diagonal lengths: Choose d₁ = 2l, then d₂ = w Or choose d₁ = l, then d₂ = 2w

Step 5: Construct rhombus with these diagonals by drawing perpendicular diagonals that bisect each other and joining their endpoints.

Exercise: Figure it Out (Section 5) | Q: 2 | (Page Page 22)
For More Understanding

Explanation

The chapter discusses dissection methods from Śulba-Sūtras. The key is to ensure the product of rhombus diagonals equals twice the rectangle's area.

Solution Steps

  1. Step 1: Rectangle area = l × w.

  2. Step 2: Rhombus area = ½ × d₁ × d₂.

  3. Step 3: Set ½ × d₁ × d₂ = l × w.

  4. Step 4: Choose appropriate diagonal lengths satisfying d₁ × d₂ = 2lw.

  5. Step 5: Construct rhombus with perpendicular diagonals of chosen lengths.

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