How do you find the maximum area of a rectangle with a fixed perimeter?
Hence the maximum area of a rectangle with given perimeter is equal to ceil(perimeter/4) * floor(perimeter/4).
How do you find maximum area from perimeter?
For a given perimeter, the area will be maximized when all the sides are the same length, which makes it actually a square. A square is still a rectangle, though! So, if you know the perimeter, divide it by four to determine the length of each side. Then multiply the length times the width to get the area.
Is the rectangle of fixed area whose perimeter is a maximum a square?
The rectangle with the largest area for a fixed perimeter is a square. A square with a perimeter of 560 feet, measures 140 feet on each side (560 feet รท 4 = 140 feet). The dimensions of the yard will be 140 feet by 140 feet and will have an area of 19,600 square feet (140 feet x 140 feet = 19600 square feet).
How do you maximize the perimeter and area?
How do you maximize the perimeter of a rectangle?
How to maximize the area of a rectangle?
For a given perimeter, the area will be maximized when all the sides are the same length, which makes it actually a square. A square is still a rectangle, though! So, if you know the perimeter, divide it by four to determine the length of each side. Then multiply the length times the width to get the area.
When to change the perimeter of a rectangle?
It turns out that, once again, the perimeter is minimized for a given area when the length and width are the same, which means that the rectangle should be a square. This will change the area of the two shapes, as you can see, but maintain the total perimeter.
How to calculate the perimeter of an area?
If you know the area and want to find the minimum perimeter possible, take the square root of the area to find the length of each side. Then, multiply the side length by four to find the total perimeter.
How big should the perimeter of a garden be?
If the garden is rectangular, it will have the largest possible area when the length equals the width. In order to have a perimeter of 100 feet, that means that each side needs to be 25 feet long. The area would then be 25ft x 25ft, or 625ft 2.