Final answer:
After accounting for the 2-meter margins all around the plot, the dimensions for fencing are reduced to 21 meters by 11 meters. The length of the fence is calculated using the perimeter formula (2l + 2w) and is found to be 64 meters.
Step-by-step explanation:
The question requires us to find the length of the fence a farmer built around a plot of land taking into account the margins left all around.
To solve this, we begin by recognizing that the original dimensions of the plot are 25 meters in length and 15 meters in width. However, since the farmer left margins of 2 meters wide all around, the actual length and width that will be fenced are reduced by 4 meters each (2m on each side for both length and width).
The adjusted dimensions of the plot are:
- Length: 25m - 2m - 2m = 21m
- Width: 15m - 2m - 2m = 11m
To find the perimeter, which is the total length of the fence, we use the formula for the perimeter:P = 2l + 2w
Substituting the adjusted dimensions into the formula:
P = 2(21m) + 2(11m)
P = 42m + 22m
P = 64m
Therefore, the length of the fence the farmer built is 64 meters.