Question 6 of 14intermediate🔧 ApplyLong Answer3 marks

Give a method to obtain a rectangle whose area is twice that of a given triangle. What are the different methods that you can think of?

Correct Answer

Method 1: Take a triangle with base b and height h. Triangle area = ½ × b × h Construct a rectangle with the same base b and same height h. Rectangle area = b × h = 2 × (½ × b × h) ∴ Rectangle area = twice the triangle's area

Method 2: Double the base while keeping the height same. Rectangle with base 2b and height h/2: Area = 2b × h/2 = b × h ∴ Rectangle area = twice the triangle's area

Method 3: By dissection, reflect the triangle across its base to form a parallelogram. Then convert to rectangle.

Exercise: Figure it Out (Section 4) | Q: 5 | (Page Page 16)
For More Understanding

Explanation

The chapter discusses various dissection and transformation methods. Since triangle area is half of base × height, a rectangle with the same base and height has twice the area.

Solution Steps

  1. Step 1: Triangle area = ½ × b × h.

  2. Step 2: Rectangle with base b and height h has area = b × h.

  3. Step 3: Rectangle area = 2 × Triangle area.

  4. Step 4: Alternative: Use base 2b with height h/2, or other combinations.

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