Fri 6 Mar, 2009 05:55 pm
Two plots of land have the same perimeter.One is a square of side 64 m and another one is rectangle of length 70 m Which plot has greater area and by how much?
A(square) = 64x64= 4096
A(rect) = 70xo.5(256-140)=70x58=4060
Note that a square is always the greatest area quadrilateral for a given perimeter.
The perimeter of the square would be 4 * 64 = 256
The rectangle would have the same perimeter.
2 sides of the rectangle are 70. So that's 2*70 =140.
The balance of the rectangle's perimeter would be 256-140 = 116.
So, the remaining 2 equal sides of the rectangle must total 116.
So, each would be 116/2 = 58.
So the area of the rectangle would be 58*70 = 4060,
while the area of the square would be 64*64 = 4096.
So, the square has the greater area, with a difference of 4096-4060 = 36.