Question

a wire is in the shape of rectangle its length is 40 cm and width 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 inclose more area and by how much

Answer 1

Length of rectangle = 40 cm
Width of rectangle = 22 cm
Area of rectangle = 40 * 22 = 880 cm^2

Perimeter of rectangle = Perimeter of square
=> Perimeter of square = 2(40+22)
=> 4*a = 2* 62
=> a = 31 cm

Side of square = 31 cm
Area of square = 31 * 31 = 961 cm^2


Square will enclose more Area than rectangle and the difference is 81 cm^2

Answer 2

length of the rectangle= 40cm
breadth of the rectangle = 22cm

perimeter = 2( length + breadth)
= 2 ( 40 + 22)
= 2( 62 )
= 124 cm

why did we find perimeter and not area??
this is because the wire is rebent, thus , we have to find the boundary of the rectangle.
Also , the square will also have same perimeter.

Perimeter of square = 4 × side
124 = 4 × side

$\frac{124}{4} = side \:$
side = 31.

The 2nd part of the question


Area of rectangle = length × breadth
= 40 × 22
= 880cm²

Area of square = side × side
= 31 × 31
= 961 cm²

it can be seen that the area of square is greater than area of rectangle
difference between area = 961cm² - 880cm²
= 81cm²

Therefore,

The area of square is greater than the area of rectangle by 81cm²