Question 21 of 21advanced🔍 AnalyzeMCQ2 marks

A square piece of paper is folded in half. The square is then cut into two rectangles along the fold. Regardless of the size of the square, one of the following statements is always true. Which statement is true here?

Exercise: Figure it Out (Section 6) | Q: 8 | (Page Page 21)
For More Understanding

Explanation

Let the side of the square be 's'. Area of square = s². When folded and cut, each rectangle has dimensions s × (s/2). Area of each rectangle = s × s/2 = s²/2. Total area of both rectangles = s² (same as square). Perimeter of square = 4s. Perimeter of each rectangle = 2 × (s + s/2) = 2 × (3s/2) = 3s. Total perimeter of both rectangles = 2×32 \times 3s = 6s. Ratio = 6s/4s = 6/4 = 1½ times.

Solution Steps

  1. Step 1: Let side of square = s. Perimeter of square = 4s

  2. Step 2: When cut into two rectangles, each has dimensions s × (s/2)

  3. Step 3: Perimeter of each rectangle = 2 × (s + s/2) = 2 × (3s/2) = 3s

  4. Step 4: Total perimeter of both rectangles = 2×32 \times 3s = 6s

  5. Step 5: Ratio = 6s : 4s = 6 : 4 = 1½ : 1

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