A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,220 ft. Determine the flag's width and length if the length is 370 ft greater than the width.
Let's assume the width of the flag as x ft.
According to the given information, the length of the flag is 370 ft greater than the width. So, the length can be represented as (x + 370) ft.
The perimeter of the flag is calculated by adding the lengths of all four sides.
Perimeter = 2*(Width + Length)
In this case, the perimeter is given as 2,220 ft. So, we can write:
2,220 = 2*(x + (x + 370))
Now, let's solve the equation to find the value of x.
2,220 = 2*(2x + 370)
Dividing both sides by 2:
1,110 = 2x + 370
Subtracting 370 from both sides:
1,110 - 370 = 2x
740 = 2x
Dividing both sides by 2:
370 = x
So, the width of the flag is 370 ft.
Now, we can calculate the length by adding 370 ft to the width:
Length = Width + 370
Length = 370 + 370
Length = 740 ft
Therefore, the width of the flag is 370 ft and the length is 740 ft.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the width of the flag is represented by the variable "w" in feet. Since the length is 370 ft greater than the width, the length can be represented by "w + 370" ft.
The perimeter of a rectangle is given by the formula: P = 2w + 2l, where P is the perimeter, w is the width, and l is the length.
In this case, the perimeter is given as 2,220 ft, so we can set up the equation as:
2w + 2(w + 370) = 2,220
Simplifying the equation:
2w + 2w + 740 = 2,220
Combining like terms:
4w + 740 = 2,220
Now, we can isolate the variable:
4w = 2,220 - 740
4w = 1,480
Dividing both sides by 4:
w = 1,480 / 4
w = 370 ft
So, the width of the flag is 370 ft.
To find the length, we use the expression w + 370:
l = w + 370
l = 370 + 370
l = 740 ft
Therefore, the length of the flag is 740 ft. So, the width of the flag is 370 ft and the length is 740 ft.