A rectangular field is 60 yards wide and 100 yards long.Give the length and width of another rectangular field that has the same perimeter but a larger area.width = yardslength = yards
Question
A rectangular field is 60 yards wide and 100 yards long.Give the length and width of another rectangular field that has the same perimeter but a larger area.width = yardslength = yards
Solution
The perimeter of a rectangle is given by the formula 2*(length + width).
For the given rectangle, the perimeter is 2*(60 yards + 100 yards) = 320 yards.
If we want another rectangle with the same perimeter but a larger area, we need to adjust the length and width such that the product of the length and width (which gives the area) is maximized.
The maximum area of a rectangle given a fixed perimeter is achieved when the rectangle is a square. This is because for a fixed perimeter, the area of a rectangle (length*width) is maximized when length = width.
So, to maximize the area, we should set the length and width to be equal.
Therefore, the length and width of the rectangle should each be half of the perimeter, which is 320 yards / 2 = 160 yards.
So, the length and width of the rectangle that has the same perimeter but a larger area are both 160 yards.
Similar Questions
rectangular field is 115 meters long and 80 meters wide.Give the length and width of another rectangular field that has the same perimeter but a smaller area.
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.
A rectangular park is 85 yards wide and 135 yards long. Give the length and width of another rectangular park that has the same perimeter but a smaller area.
A rectangular lot is 60 meters wide and 105 meters long.Give the length and width of another rectangular lot that has the same perimeter but a smaller area.
A farmer wants to fence an area of 3750 square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the amount of fencing needed? ft (smaller value) ft (larger value)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.