A rectangular lot is 120 yards long and 75 yards wide.Give the length and width of another rectangular lot that has the same perimeter but a larger area.
Question
A rectangular lot is 120 yards long and 75 yards wide.Give the length and width of another rectangular lot that has the same perimeter but a larger area.
Solution
The perimeter of the given rectangular lot is 2*(length + width) = 2*(120 yards + 75 yards) = 390 yards.
To have a larger area with the same perimeter, the length and width of the new rectangular lot should be closer to each other. This is because for a given perimeter, a square has the maximum area.
So, let's take the average of the length and width of the original rectangle as the length and width of the new rectangle.
Average = (120 yards + 75 yards) / 2 = 97.5 yards.
So, the length and width of another rectangular lot that has the same perimeter but a larger area would be 97.5 yards by 97.5 yards.
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