a rectangular garden 9ft by 12 ft includes a uniform border of wood chips around a rectangular bed of flowers. If flowers take up half the garden's area. find the perimeter of the flower bed
A = 9 * 12
A = 108 square feet
108/2 = 54
Flower bed is 6 ft by 9 ft
P = 12 + 18 = 30 feet
What is the area of the garden that measures 9ft. By 12ft.
To find the perimeter of the flower bed, we first need to determine the area occupied by the flowers. Given that the flowers take up half the garden's area, we can calculate the area of the garden as follows:
Area of the garden = length * width
Area of the garden = 9 ft * 12 ft
Area of the garden = 108 square ft
Since the flowers occupy half the area, the area of the flower bed is half of the garden's area:
Area of the flower bed = 1/2 * 108 square ft
Area of the flower bed = 54 square ft
Now let's calculate the dimensions of the flower bed. Since the garden has a uniform border of wood chips around the flower bed, we can subtract twice the border width from the original dimensions of the garden to get the dimensions of the flower bed.
Let's assume the border width is "b" feet. Therefore, the length of the flower bed will be:
Length of the flower bed = length of garden - 2 * border width
Length of the flower bed = 9 ft - 2 * b ft
Length of the flower bed = 9 ft - 2b ft
Similarly, the width of the flower bed will be:
Width of the flower bed = width of garden - 2 * border width
Width of the flower bed = 12 ft - 2 * b ft
Width of the flower bed = 12 ft - 2b ft
Now, we can find the perimeter of the flower bed by adding up all four sides:
Perimeter of the flower bed = 2 * length of the flower bed + 2 * width of the flower bed
Perimeter of the flower bed = 2(9 ft - 2b ft) + 2(12 ft - 2b ft)
Perimeter of the flower bed = 18 ft - 4b ft + 24 ft - 4b ft
Perimeter of the flower bed = (18 + 24) ft - (4b + 4b) ft
Perimeter of the flower bed = 42 ft - 8b ft
Therefore, the perimeter of the flower bed is 42 ft - 8b ft.
To find the perimeter of the flower bed, we first need to determine the dimensions of the flower bed itself.
Given that the garden is 9ft by 12ft, we can calculate its area: A = length * width = 9ft * 12ft = 108 sq ft.
Since the flower bed takes up half of the garden's area, the flower bed occupies an area of 108 sq ft / 2 = 54 sq ft.
Let's represent the dimensions of the flower bed as L and W. We know that the length and width of the flower bed will be smaller than the garden, so we can assume L < 9ft and W < 12ft.
To find the possible dimensions of the flower bed, we need to find two numbers that multiply together to give 54. Some factors of 54 are: 1, 2, 3, 6, 9, 18, 27, and 54.
Let's check which combinations of these factors satisfy the condition L < 9ft and W < 12ft:
1) L = 1ft, W = 54ft: Not valid as W > 12ft.
2) L = 2ft, W = 27ft: Valid as L < 9ft and W < 12ft.
3) L = 3ft, W = 18ft: Valid as L < 9ft and W < 12ft.
4) L = 6ft, W = 9ft: Not valid as L > 9ft.
5) L = 9ft, W = 6ft: Not valid as W > 12ft.
6) L = 18ft, W = 3ft: Valid as L < 9ft and W < 12ft.
7) L = 27ft, W = 2ft: Not valid as L > 9ft.
8) L = 54ft, W = 1ft: Not valid as L > 9ft.
We find that the valid combinations for the flower bed dimensions are (2ft, 27ft) and (3ft, 18ft), and their respective perimeters are:
Perimeter = 2 * (L + W)
1) For (2ft, 27ft):
Perimeter = 2 * (2ft + 27ft) = 2 * 29ft = 58ft.
2) For (3ft, 18ft):
Perimeter = 2 * (3ft + 18ft) = 2 * 21ft = 42ft.
Therefore, the possible perimeters of the flower bed are 58ft and 42ft.