Question

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?
​

Answer 1

1) let the rectangle length =l =40cm

breadth =b =22 cm

let the side of a square = a cm

if the same wire is rebent in the shape of a square then

perimeter of a square=perimeter of rectangle

4a=2(l+b)

4a =2(40+22)

4a =2*62

a =2*62/4

a=31 cm

therefore side of a square = a =31cm

2) area of the rectangle =l*b= 40*22=880 cm^2

3)area of the square=a^2 = (31)^2 =961 cm^2

therefore

area of the square is more

Answer 2

Length of rectangle = 40 m

and breadth = 22 cm

perimeter = 2(40+22) = 2×62 = 124cm

perimeter of square wire = 124 cm

Then side = $\frac{perimeter}{4} = \frac{124}{4} = 31m$

Now area of rectangle = 40×22 = 880cm²

and area of square = 31² = 961cm²

Difference in area = 961-880=81cm²

area of 81cm² is more of square shaped wire.