Question 8 - Figure it out - Page 149 - Chapter 6 Class 6 - Perimeter and Area (Ganita Prakash)

Transcript

Question 8 (a) 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? (a) The area of each rectangle is larger than the area of the square. Our figure looks like Here, we have to find Area of both Area of square = a × a = a2 Area of rectangle = Length × Breadth = a × 𝑎/2 = 𝒂^𝟐/𝟐 Since 𝒂^𝟐/𝟐<𝒂 Area of each rectangle (a²/2) is smaller than the square's area (a²). Thus, given statement is False Question 8 (b) 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? (b) The perimeter of the square is greater than the perimeters of both the rectangles added together. Here, we have to find Perimeter of both Perimeter of square = 4 × Side of Square = 4a Perimeter of rectangle = 2 × (Length + Breadth) = 2 × (a + 𝑎/2) = 2 × (2𝑎 + 𝑎)/2 = 2 × 3𝑎/2 = 3a Also, Perimeter of both rectangles = 2 × 3a = 6a Since 4a < 6a Perimeter of square < Perimeter of both rectangles Thus, given statement is False Question 8 (c) 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? (c) The perimeters of both the rectangles added together is always 1 1/2 times the perimeter of the square. We know that Perimeter of square = 4a Perimeter of both rectangles = 6a Finding 𝟏 𝟏/𝟐 times the perimeter of the square. Now, 𝟏 𝟏/𝟐 × 𝟒𝒂=(2 × 1 + 1)/2 × 4𝑎 =(2 + 1)/2 × 4𝑎 =3/2 × 4𝑎 = 3 × 2a = 6a = Perimeter of both rectangles Our statement was The perimeters of both the rectangles added together is always 1 1/2 times the perimeter of the square. Thus, given statement is True Question 8 (d) 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? (d) The area of the square is always three times as large as the areas of both rectangles added together.We know that Area of square = a2 Area of 1 rectangle = 𝑎^2/2 Area of both rectangles = 2 × 𝑎^2/2=𝒂^𝟐 Our statement is The area of the square is always three times as large as the areas of both rectangles added together. Since Area of square and Area of both rectangles are equal Thus, given statement is False