a rectangular dield isto be enclosed with1120ft of fencing. If the length of the field is 40ft longer than the width, then how long is the field?
90
Let's denote the width of the field as "x" feet.
According to the problem, the length of the field is 40 feet longer than the width, so the length would be (x + 40) feet.
To calculate the perimeter of the rectangular field, we need to add up all the sides.
Perimeter = 2(length) + 2(width)
In this case, the perimeter is given as 1120 feet. So we can write the equation as:
1120 = 2(x + 40) + 2x
Simplifying this equation:
1120 = 2x + 80 + 2x
1120 = 4x + 80
Subtracting 80 from both sides:
1040 = 4x
Dividing both sides by 4:
x = 260
Therefore, the width of the field is 260 feet.
To find the length, we can substitute the value of x into the equation for the length:
length = x + 40 = 260 + 40 = 300
Therefore, the length of the field is 300 feet.
To find the length of the field, we'll need to set up an equation based on the information given.
Let's assume that the width of the field is "w" feet.
According to the given information, the length of the field is 40 feet longer than the width, so the length can be represented as "w + 40" feet.
The formula to calculate the perimeter (the total length of fencing needed to enclose the field) of a rectangle is:
Perimeter = 2(Length + Width)
In this case, we have:
Perimeter = 2(w + 40 + w)
Perimeter = 2(2w + 40)
Perimeter = 4w + 80
Given that the perimeter of the field is 1120 feet, we can set up an equation:
4w + 80 = 1120
To isolate "w," we'll begin by subtracting 80 from both sides of the equation:
4w = 1120 - 80
4w = 1040
Next, divide both sides by 4:
w = 1040 / 4
w = 260
Therefore, the width of the field is 260 feet.
Since we know the length is 40 feet more than the width, we can calculate it:
Length = Width + 40
Length = 260 + 40
Length = 300
Hence, the length of the field is 300 feet.
P = 2L + 2W
1120 = 2(W + 40) + 2W
1120 = 4W + 80
1040 = 4W
1040/4 = W