A rectangle and a square both have a perimeter of 20. The rectangle has a length of 6.
Which shape has a greater area? How do you know?
The square has a perimeter of 20, so its side is 5
then its area is 25 units square, the same a the rectangle
the rectangle is
length x width
= 6w = 25
w = 25/6 units
Thanks!
To find out which shape has a greater area, we need to compare the areas of the rectangle and the square.
First, let's calculate the dimensions of the rectangle. We know that a rectangle's perimeter is calculated by adding up all of its side lengths. In this case, the perimeter of the rectangle is 20. We are also given that the length of the rectangle is 6.
To find the width of the rectangle, we can use the formula for the perimeter of a rectangle:
Perimeter = 2 * (Length + Width)
20 = 2 * (6 + Width)
20 = 12 + 2 * Width
2 * Width = 20 - 12
2 * Width = 8
Width = 8 / 2
Width = 4
So, the dimensions of the rectangle are length = 6 and width = 4.
Now, let's calculate the area of the rectangle using the formula:
Area = Length * Width
Area = 6 * 4
Area = 24
Next, let's move on to the square. Since we know the perimeter is 20, we can calculate the side length of the square by dividing the perimeter by 4 (because a square has four equal sides):
Side length = Perimeter / 4
Side length = 20 / 4
Side length = 5
Now that we have the side length of the square, we can calculate its area using the formula:
Area = Side length * Side length
Area = 5 * 5
Area = 25
Therefore, comparing the areas of the rectangle and the square, we can see that the square has a greater area since its area is 25, whereas the rectangle's area is 24.
In conclusion, the square has a greater area than the rectangle.