Question 1 of 14intermediate🔧 ApplyLong Answer3 marks

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

Correct Answer

Method 1: Using the Diagonal

Step 1: Take rectangle ABCD with base = b and height = h.

Step 2: Draw diagonal AC.

Step 3: The diagonal divides the rectangle into two congruent triangles, each with area = ½ × b × h.

Method 2: Triangle with Same Base and Double Height

Step 1: Extend one side and join opposite vertices to create a triangle with base = b and height = 2h.

Step 2: Area = ½ × b × 2h = b × h (same as rectangle area).

Exercise: Figure it Out (Section 2) | Q: 4 | (Page Page 11)
For More Understanding

Explanation

The Śulba-Sūtras are ancient Indian geometric texts dealing with construction of altars. The chapter mentions that such transformations were important for altar construction. The diagonal of a rectangle divides it into two triangles of equal area, each being half the rectangle's area.

Solution Steps

  1. Take rectangle ABCD with base = b and height = h.

  2. Draw diagonal AC.

  3. The diagonal divides the rectangle into two congruent triangles, each with area = ½ × b × h.

  4. Extend one side and join opposite vertices to create a triangle with base = b and height = 2h.

  5. Area = ½ × b × 2h = b × h (same as rectangle area).

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