A = length * width
40 * 10 = 400 sq. ft
Try a square and a circle.
http://www.mathsisfun.com/area.html
I need to get the largest area of 100 feet of rope. I want to say rectangle: 40L x 40L x 10w x 10w =100
Please advise if I am on the right track. Keeping in mind that you can use any Plan Geometry Shape?
3 answers
*--Considering all rectangles with the same perimeter, the square encloses the greatest area.
Proof: Consider a square of dimensions x by x, the area of which is x^2. Adjusting the dimensions by adding a to one side and subtracting a from the other side results in an area of (x + a)(x - a) = x^2 - a^2. Thus, however small the dimension "a" is, the area of the modified rectangle is always less than the square of area x^2.
*--Considering all rectangles with the same area, the square results in the smallest perimeter for a given area.
*--Considering all shapes, the circle encloses the maximum area for a given perimeter.
Proof: Consider a square of dimensions x by x, the area of which is x^2. Adjusting the dimensions by adding a to one side and subtracting a from the other side results in an area of (x + a)(x - a) = x^2 - a^2. Thus, however small the dimension "a" is, the area of the modified rectangle is always less than the square of area x^2.
*--Considering all rectangles with the same area, the square results in the smallest perimeter for a given area.
*--Considering all shapes, the circle encloses the maximum area for a given perimeter.
The geometric figure that encloses the most area is a circle.
A circumference C=100=2pi r so r=15.92 and
Area = pi r^2 = 795.77
Your rectangle of 40*10 = only 400 sq. ft.
A perimeter of 25 feet per side times 4 sides = a length of rope 100 feet long and encloses the greatest area for an oblong figure, of 25^2 = 625 feet.
Clearly, the circle is a vast improvement, by 795.77/625=127.32%
An ellipse is not more efficient than a circle.
The reason is that a circle uses only one leg or end to multiply by, whereas other figures involve multiple generators or legs or multipliers. A radius is fixed at one end. But when you multiply down a rectangle, you are really moving the width (with its TWO ENDS) along the entire Length (with its TWO ENDS)! That is less efficient. The saved energy shows up in the area conserved.
A circumference C=100=2pi r so r=15.92 and
Area = pi r^2 = 795.77
Your rectangle of 40*10 = only 400 sq. ft.
A perimeter of 25 feet per side times 4 sides = a length of rope 100 feet long and encloses the greatest area for an oblong figure, of 25^2 = 625 feet.
Clearly, the circle is a vast improvement, by 795.77/625=127.32%
An ellipse is not more efficient than a circle.
The reason is that a circle uses only one leg or end to multiply by, whereas other figures involve multiple generators or legs or multipliers. A radius is fixed at one end. But when you multiply down a rectangle, you are really moving the width (with its TWO ENDS) along the entire Length (with its TWO ENDS)! That is less efficient. The saved energy shows up in the area conserved.
0 answers