To find the length and width of another rectangular field with the same perimeter but a larger area, we can use the formula for the perimeter and area of a rectangle.
Given:
Length of the original rectangular field = 105 meters
Width of the original rectangular field = 55 meters
Perimeter of the original rectangular field = 2 * (Length + Width)
= 2 * (105 + 55)
= 2 * 160
= 320 meters
Now, let's consider the length and width of the new rectangular field as variables (L and W, respectively).
To maintain the same perimeter, the sum of the length and width of the new field should also be 320 meters.
Therefore, we can set up the following equation:
L + W = 320
To find the dimensions that maximize the area, we need to find the values of L and W that satisfy this equation and result in the largest possible product LW (area).
To find the maximum area, we can use the fact that the area of a rectangle is maximized when the length and width are equal.
Therefore, we set L = W to maximize the area.
Substituting L = W into the equation L + W = 320:
W + W = 320
2W = 320
W = 160
Thus, the width of the new rectangular field is 160 meters.
Substituting W = 160 into L + W = 320:
L + 160 = 320
L = 320 - 160
L = 160
Hence, the length of the new rectangular field is also 160 meters.
In summary, the length and width of another rectangular field that has the same perimeter but a larger area are both 160 meters.
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