Length = 200 feet
Width = 140 feet
We can solve this problem without using matrices as it doesn't involve matrix operations directly. However, we can set up equations and solve them systematically.
Let:
l be the length of the plot in feet.
w be the width of the plot in feet.
Given information:
Perimeter = 680 feet (P)
l = w + 60 feet
Steps to solve:
Express the perimeter in terms of l and w:
The perimeter is the sum of the lengths of all sides of the rectangle: P = 2l + 2w
Substitute the second equation into the first equation:
P = 2(w + 60) + 2w
Simplify the equation:
P = 4w + 120
Plug in the given perimeter value:
680 = 4w + 120
Solve for w:
Subtract 120 from both sides: 560 = 4w
Divide both sides by 4: w = 140 feet
Calculate the length using the second equation:
l = w + 60 = 140 + 60 = 200 feet
Therefore, the length of the plot is 200 feet and the width is 140 feet.
The dimensions of the rectangular plot are a width of 140 feet and a length of 200 feet. This was determined by setting up and solving equations based on the perimeter and the relationship between length and width. The length is 60 feet longer than the width.
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