A rectangular field is to be enclosed with 1270 ft of fencing. If the length of the field is 75 ft longer
than the width, then how wide is the field?
A) 430 ft B) 355 ft C) 280 ft D) 385 ft
P = 2L + 2W
1270 = 2(W + 75) + 2W
1270 = 4W + 150
1120 = 4W
280 = W
To solve this problem, we can start by setting up expressions for the perimeter of the rectangular field. Let's assume that the width of the field is 'w' ft.
According to the given information, the length of the field is 75 ft longer than the width. So, the length can be expressed as 'w + 75' ft.
The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, we have two equal lengths (w + 75) ft each and two equal widths (w) ft each.
The total perimeter is given as 1270 ft. So, we can set up an equation:
2(w + 75) + 2w = 1270
Simplifying the equation, we get:
2w + 150 + 2w = 1270
4w + 150 = 1270
Subtracting 150 from both sides, we get:
4w = 1120
Dividing both sides by 4, we get:
w = 280
So, the width of the field is 280 ft.
Therefore, the correct answer is option C) 280 ft.