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
AAAaannndd the bot gets it wrong yet again!
A,D,E
To find rectangles with the same perimeters but smaller areas than the given rectangle, we need to compare the perimeters and areas of the given rectangle with those of the other rectangles listed.
First, let's calculate the perimeter and area of the given rectangle with length 5 ft and height 6 ft:
Perimeter = 2 * (length + height)
Perimeter = 2 * (5 ft + 6 ft) = 2 * (11 ft) = 22 ft
Area = length * height
Area = 5 ft * 6 ft = 30 ft²
Now, let's compare the perimeters and areas of the other rectangles:
A. Rectangle with 8 ft length and 3 ft width:
Perimeter = 2 * (length + width)
Perimeter = 2 * (8 ft + 3 ft) = 2 * (11 ft) = 22 ft
Area = length * width
Area = 8 ft * 3 ft = 24 ft²
Since the perimeter is the same but the area is smaller than the given rectangle, option A is correct.
B. Rectangle with 6 ft length and 4 ft width:
Perimeter = 2 * (length + width)
Perimeter = 2 * (6 ft + 4 ft) = 2 * (10 ft) = 20 ft
Area = length * width
Area = 6 ft * 4 ft = 24 ft²
Since the perimeter is smaller than the given rectangle but the area is the same, option B is not correct.
C. Rectangle with 10 ft length and 3 ft width:
Perimeter = 2 * (length + width)
Perimeter = 2 * (10 ft + 3 ft) = 2 * (13 ft) = 26 ft
Area = length * width
Area = 10 ft * 3 ft = 30 ft²
Since both the perimeter and area are larger than the given rectangle, option C is not correct.
D. Rectangle with 7 ft length and 4 ft width:
Perimeter = 2 * (length + width)
Perimeter = 2 * (7 ft + 4 ft) = 2 * (11 ft) = 22 ft
Area = length * width
Area = 7 ft * 4 ft = 28 ft²
Since the perimeter is the same but the area is larger than the given rectangle, option D is not correct.
E. Rectangle with 9 ft length and 2 ft width:
Perimeter = 2 * (length + width)
Perimeter = 2 * (9 ft + 2 ft) = 2 * (11 ft) = 22 ft
Area = length * width
Area = 9 ft * 2 ft = 18 ft²
Since both the perimeter and area are smaller than the given rectangle, option E is correct.
Therefore, the rectangles with the same perimeters but smaller areas than the given rectangle are options A and E.
B, D, E
Which of the following rectangles has the same perimeter as the one shown above?
A.
a rectangle with a height of 5 cm and width of 3 cm
B.
a rectangle with a height of 9 cm and width of 2 cm
C.
a rectangle with a height of 7 cm and a width of 3 cm
D.
a rectangle with a height of 8 cm and a width of 5 cm