Question 3 of 5
Which size rectangles have the same perimeters but smaller areas than the one shown below? Select all that apply.
A rectangle is shown with a length of 5 ft and height as 6 ft.
A.8 feet long and 3 feet wide
B.6 feet long and 4 feet wide
C.10 feet long and 3 feet wide
D.7 feet long and 4 feet wide
E.9 feet long and 2 feet wide
A, C, and E are the rectangles that have the same perimeters but smaller areas than the one shown.
To find the rectangles with the same perimeters but smaller areas than the given rectangle, we need to compare the dimensions of each option to the given rectangle.
1. Option A: 8 feet long and 3 feet wide
To calculate the perimeter: 2 * (length + width) = 2 * (8ft + 3ft) = 22ft
To calculate the area: length * width = 8ft * 3ft = 24ft^2 (larger area than the given rectangle)
2. Option B: 6 feet long and 4 feet wide
To calculate the perimeter: 2 * (length + width) = 2 * (6ft + 4ft) = 20ft
To calculate the area: length * width = 6ft * 4ft = 24ft^2 (larger area than the given rectangle)
3. Option C: 10 feet long and 3 feet wide
To calculate the perimeter: 2 * (length + width) = 2 * (10ft + 3ft) = 26ft
To calculate the area: length * width = 10ft * 3ft = 30ft^2 (larger area than the given rectangle)
4. Option D: 7 feet long and 4 feet wide
To calculate the perimeter: 2 * (length + width) = 2 * (7ft + 4ft) = 22ft
To calculate the area: length * width = 7ft * 4ft = 28ft^2 (larger area than the given rectangle)
5. Option E: 9 feet long and 2 feet wide
To calculate the perimeter: 2 * (length + width) = 2 * (9ft + 2ft) = 22ft
To calculate the area: length * width = 9ft * 2ft = 18ft^2 (same perimeter but smaller area than the given rectangle)
Therefore, the rectangles with the same perimeters but smaller areas than the given rectangle are:
E. 9 feet long and 2 feet wide.