Draw 2 different rectangles with a the perimeter of 8cm. One rectangle has the least area. The other rectangle has the greatest area.
the largest rectangle would be the square
2W + 2L = 8
W+L=4
for a square each side is 2 cm, and the maximum area is 4 cm^2
There is no such thing as a smallest rectangle.
We can make one of the sides very very small, but there would still be an area.
e.g. suppose W = .001
then L = 3.999
and the area = .001(3.999) = .003999
We can make the area smaller and smaller without ever reaching zero.
To find two rectangles with a perimeter of 8 cm, we need to consider different combinations of side lengths that add up to 8 cm. Since we want to find the rectangle with the smallest area, we start with the smallest possible side lengths.
Step 1: Start with the smallest side lengths
Let's start with the smallest side lengths that can make up a perimeter of 8 cm. We choose 1 cm for one side length and 3 cm for the other side length.
Step 2: Calculate the area of the rectangle with the smallest side lengths
To find the area of a rectangle, we multiply the length by the width. In this case, the length is 3 cm and the width is 1 cm.
Area = length * width = 3 cm * 1 cm = 3 cm^2
So, the rectangle with the smallest area has side lengths of 1 cm and 3 cm, and its area is 3 square cm.
Step 3: Calculate the side lengths for the rectangle with the greatest area
To find the rectangle with the greatest area, we need to consider the case where the side lengths are equal. Since the perimeter is 8 cm, we divide it by 4 to get the length of one side.
Length of one side = Perimeter / 4 = 8 cm / 4 = 2 cm
Step 4: Calculate the area of the rectangle with the greatest side lengths
To find the area of a square, we multiply the length of one side by itself.
Area = side length * side length = 2 cm * 2 cm = 4 cm^2
So, the rectangle with the greatest area has side lengths of 2 cm and 2 cm, and its area is 4 square cm.
Therefore, the rectangle with the least area has side lengths 1 cm and 3 cm, and the rectangle with the greatest area has side lengths 2 cm and 2 cm.
To find the answer, we need to consider the formula for the perimeter and the area of a rectangle.
Perimeter of a rectangle = 2 * (length + width)
Area of a rectangle = length * width
Let's start by finding the rectangle with the least area.
To minimize the area, let's choose one side of the rectangle to be as small as possible. Let's set the length of the rectangle to be 1 cm.
Using the formula for the perimeter, we have:
2 * (1 + width) = 8
2 + 2 * width = 8
2 * width = 6
width = 6 / 2
width = 3 cm
So, the dimensions of the rectangle with the least area are: length = 1 cm and width = 3 cm.
Next, let's find the rectangle with the greatest area.
To maximize the area, let's choose both sides to be equal. Let's set the length of the rectangle to be 4 cm.
Using the formula for the perimeter, we have:
2 * (4 + width) = 8
8 + 2 * width = 8
2 * width = 8 - 8
2 * width = 0
width = 0 / 2
width = 0 cm
Since width cannot be negative, we cannot have a rectangle with both sides equal to 4 cm. Therefore, there is no rectangle with the greatest area that has a perimeter of 8 cm.
To summarize:
Rectangle with the least area: length = 1 cm, width = 3 cm
No rectangle with the greatest area exists given the constraints.