Which size rectangle has the same area but a greater perimeter than the one shown below?
A rectangle is shown with a length and height of 4 ft.
A.6 feet long and 2 feet wide
B.7 feet long and 1 foot wide
C.5 feet long and 3 feet wide
D.8 feet long and 2 feet wide
C. 5 feet long and 3 feet wide.
The area of the original rectangle is 4 ft x 4 ft = 16 square feet.
The perimeter of the original rectangle is 2(4 ft + 4 ft) = 16 feet.
For option A, the area would still be 16 square feet (6 ft x 2 ft), but the perimeter would be 2(6 ft + 2 ft) = 16 feet, the same as the original rectangle.
For option B, the area would still be 16 square feet (7 ft x 1 ft), but the perimeter would be 2(7 ft + 1 ft) = 16 feet, the same as the original rectangle.
For option D, the area would still be 16 square feet (8 ft x 2 ft), but the perimeter would be 2(8 ft + 2 ft) = 20 feet, greater than the original rectangle.
Option C gives a rectangle with an area of 15 square feet (5 ft x 3 ft), which is still equal to the original rectangle. However, the perimeter would be 2(5 ft + 3 ft) = 16 feet, greater than the original rectangle. Therefore, C is the correct answer.