A farmer needs to fence a rectangular piece of land.She wants the length of the field to be 55 feet longer than the width. If she has 1310 feet of fencing material, what should be the length and the width of the field?
P = 2L + 2W
1310 = 2(W + 55) + 2W
1310 = 4W + 110
1200 = 4W
300 = W
Let's denote the width of the field as "x" (in feet).
According to the problem, the length of the field is 55 feet longer than the width. Therefore, the length would be x + 55.
Now, let's calculate the perimeter of the rectangular piece of land:
Perimeter = 2(length) + 2(width)
Since there are four sides of equal lengths in a rectangle, multiplying by 2 is necessary here.
The perimeter is given as 1310 feet, therefore we can write:
1310 = 2(x + 55) + 2x
Simplifying the equation:
1310 = 2x + 110 + 2x
Combining like terms:
1310 = 4x + 110
Subtracting 110 from both sides:
1200 = 4x
Dividing both sides by 4:
x = 300
So, the width of the field is 300 feet.
Now, we can find the length by substituting x back into the expression x + 55:
Length = x + 55
Length = 300 + 55
Length = 355
Therefore, the length of the field is 355 feet and the width is 300 feet.
To solve this problem, we can set up an equation based on the given information.
Let's assume the width of the field is x feet.
According to the problem, the length of the field is 55 feet longer than the width, so the length would be (x + 55) feet.
The perimeter of a rectangle is given by the formula: 2(length + width).
In this case, the perimeter of the field is 1310 feet, so we can set up the equation:
2(x + (x + 55)) = 1310
Now, let's solve the equation step by step:
2(2x + 55) = 1310
4x + 110 = 1310
4x = 1310 - 110
4x = 1200
x = 1200 / 4
x = 300
Therefore, the width of the field is 300 feet.
Now, let's find the length:
Length = x + 55
Length = 300 + 55
Length = 355
Therefore, the length of the field is 355 feet and the width is 300 feet.