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 rect=40cm
breadth of rect=22cm
area=40cm×22cm
=880cm square
length of wire=2 (l+b)
2×(40cm+22cm)
2×62
124cm

side of a square=124cm/4
=31cm
area=31cm×31cm
=961cm square
shape enclosing more area=961cm square -880cm square
=by 81cm square