A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area?
First, the perimeter of the wire = Perimeter of the rectangle = 2 (l + b) = 2 x (40 cm + 22 cm) = 2 x 62 cm = 124 cm
Then, the perimeter of the square = 124 cm
The side length of the square = (124/4) cm = 31 cm
Area of the rectangle = l x b = 40 cm x 22 cm = 880 cm^2
Area of the square = s^2 = 31 cm x 31 cm = 961 cm^2
This proves that the square encloses more area than the rectangle.
By the way, whenever you have a certain perimeter length, the largest quadrilateral that has this perimeter is always a square.