Multiple Representations Use the grid to draw three different rectangles so that each has an area of 12 square units and they all hav different widths. What are the dimensions of the rectangles?

To find three different rectangles with an area of 12 square units and different widths, we can use the formula for the area of a rectangle: \[ A = w \times h \] where \( A \) is the area, \( w \) is the width, and \( h \) is the height. Given that the area \( A = 12 \), we can express the height in terms of the width: \[ h = \frac{A}{w} = \frac{12}{w} \] Now, we will choose different widths \( w \) and calculate the corresponding heights \( h \) for each rectangle. The width must be a positive factor of 12 to ensure that the height is also a positive integer. The factors of 12 are: 1, 2, 3, 4, 6, and 12. We will select three different widths from these factors. 1. **Width \( w = 1 \)**: \[ h = \frac{12}{1} = 12 \] Dimensions: \( 1 \times 12 \) 2. **Width \( w = 2 \)**: \[ h = \frac{12}{2} = 6 \] Dimensions: \( 2 \times 6 \) 3. **Width \( w = 3 \)**: \[ h = \frac{12}{3} = 4 \] Dimensions: \( 3 \times 4 \) Now we have three rectangles with different widths and the same area of 12 square units: 1. Rectangle 1: \( 1 \times 12 \) 2. Rectangle 2: \( 2 \times 6 \) 3. Rectangle 3: \( 3 \times 4 \) These rectangles can be drawn on a grid, and their dimensions are as follows: - Rectangle 1: Width = 1, Height = 12 - Rectangle 2: Width = 2, Height = 6 - Rectangle 3: Width = 3, Height = 4 Each rectangle has a unique width and an area of 12 square units.